{"id":1935,"date":"2018-12-11T13:40:58","date_gmt":"2018-12-11T13:40:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/chapter\/graphs-of-functions\/"},"modified":"2020-05-17T05:56:26","modified_gmt":"2020-05-17T05:56:26","slug":"graphs-of-functions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/chapter\/graphs-of-functions\/","title":{"raw":"Graphs of Functions","rendered":"Graphs of Functions"},"content":{"raw":"[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3>Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Use the vertical line test<\/li><li>Identify graphs of basic functions<\/li><li>Read information from a graph of a function<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1167826157468\" class=\"be-prepared\"><p id=\"fs-id1167830095706\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167836665273\" type=\"1\"><li>Evaluate: <span class=\"token\">\u24d0<\/span> \\({2}^{3}\\) <span class=\"token\">\u24d1<\/span> \\({3}^{2}.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829586631\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Evaluate: <span class=\"token\">\u24d0<\/span> \\(|7|\\) <span class=\"token\">\u24d1<\/span> \\(|-3|.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/05eab039-6d1c-4d80-8c8c-94469164a52c#fs-id1167835365552\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Evaluate: <span class=\"token\">\u24d0<\/span> \\(\\sqrt{4}\\) <span class=\"token\">\u24d1<\/span> \\(\\sqrt{16}.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167833056590\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836579284\"><h3 data-type=\"title\">Use the Vertical Line Test<\/h3><p id=\"fs-id1167829579930\">In the last section we learned how to determine if a relation is a function. The relations we looked at were expressed as a set of ordered pairs, a mapping or an equation. We will now look at how to tell if a graph is that of a function.<\/p><p id=\"fs-id1167836691995\">An ordered pair \\(\\left(x,y\\right)\\) is a solution of a linear equation, if the equation is a true statement when the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-values of the ordered pair are substituted into the equation.<\/p><p id=\"fs-id1167829924871\">The graph of a linear equation is a straight line where every point on the line is a solution of the equation and every solution of this equation is a point on this line.<\/p><p id=\"fs-id1167836625879\">In <a href=\"#CNX_IntAlg_Figure_03_06_001\" class=\"autogenerated-content\">(Figure)<\/a>, we can see that, in graph of the equation \\(y=2x-3,\\) for every <em data-effect=\"italics\">x<\/em>-value there is only one <em data-effect=\"italics\">y<\/em>-value, as shown in the accompanying table.<\/p><div class=\"bc-figure figure\" id=\"CNX_IntAlg_Figure_03_06_001\"><span data-type=\"media\" id=\"fs-id1167836424063\" data-alt=\"plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled y equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label y equals2 x minus 3. The second row is a header row with the headers x, y, and (x, y). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2018\/12\/CNX_IntAlg_Figure_03_06_001_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled y equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label y equals2 x minus 3. The second row is a header row with the headers x, y, and (x, y). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><\/span><\/div><p>A relation is a function if every element of the domain has exactly one value in the range. So the relation defined by the equation \\(y=2x-3\\) is a function.<\/p><p>If we look at the graph, each vertical dashed line only intersects the line at one point. This makes sense as in a function, for every <em data-effect=\"italics\">x<\/em>-value there is only one <em data-effect=\"italics\">y<\/em>-value.<\/p><p id=\"fs-id1167836600350\">If the vertical line hit the graph twice, the <em data-effect=\"italics\">x<\/em>-value would be mapped to two <em data-effect=\"italics\">y<\/em>-values, and so the graph would not represent a function.<\/p><p id=\"fs-id1167836293137\">This leads us to the vertical line test. A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point. If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/p><div data-type=\"note\" id=\"fs-id1167833386905\"><div data-type=\"title\">Vertical Line Test<\/div><p>A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point.<\/p><p id=\"fs-id1167836608075\">If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/p><\/div><div data-type=\"example\" id=\"fs-id1167836731467\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836579319\"><div data-type=\"problem\"><p id=\"fs-id1167836646294\">Determine whether each graph is the graph of a function.<\/p><span data-type=\"media\" id=\"fs-id1167836552272\" data-alt=\"The figure has two graphs. In graph a there is a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). In graph b there is a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_002_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). In graph b there is a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833102413\"><p id=\"fs-id1167836542012\"><span class=\"token\">\u24d0<\/span> Since any vertical line intersects the graph in at most one point, the graph is the graph of a function.<\/p><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167836557713\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 5, x equalsnegative 3, and x equals3. Each line intersects the slanted line at exactly one point.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_003_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 5, x equalsnegative 3, and x equals3. Each line intersects the slanted line at exactly one point.\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> One of the vertical lines shown on the graph, intersects it in two points. This graph does not represent a function.<div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167833339591\" data-alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 2, x equalsnegative 1, and x equals2. The vertical line x \u2013 negative 2 does not intersect the parabola. The vertical line x equalsnegative 1 intersects the parabola at exactly one point. The vertical line x equals3 intersects the parabola at two separate points.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_004_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 2, x equalsnegative 1, and x equals2. The vertical line x \u2013 negative 2 does not intersect the parabola. The vertical line x equalsnegative 1 intersects the parabola at exactly one point. The vertical line x equals3 intersects the parabola at two separate points.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836289482\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167830123185\"><div data-type=\"problem\" id=\"fs-id1167836439913\"><p id=\"fs-id1167836333903\">Determine whether each graph is the graph of a function.<\/p><span data-type=\"media\" id=\"fs-id1167836728309\" data-alt=\"The figure has two graphs. In graph a there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (0, negative 1), (negative 1, 0), (1, 0), (negative 2, 3), and (2, 3). In graph b there is a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 2, 0), (2, 0), (0, negative 2), and (0, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_005_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (0, negative 1), (negative 1, 0), (1, 0), (negative 2, 3), and (2, 3). In graph b there is a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 2, 0), (2, 0), (0, negative 2), and (0, 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833061214\"><p id=\"fs-id1167829879758\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> no<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836537878\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836519221\"><div data-type=\"problem\" id=\"fs-id1167836526902\"><p id=\"fs-id1167836626524\">Determine whether each graph is the graph of a function.<\/p><span data-type=\"media\" data-alt=\"The figure has two graphs. In graph a there is an ellipse graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The ellipse goes through the points (0, negative 3), (negative 2, 0), (2, 0), and (0, 3). In graph b there is a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (2, 0), and (4, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_006_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is an ellipse graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The ellipse goes through the points (0, negative 3), (negative 2, 0), (2, 0), and (0, 3). In graph b there is a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (2, 0), and (4, 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836700357\"><p id=\"fs-id1167829693572\"><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\"><h3 data-type=\"title\">Identify Graphs of Basic Functions<\/h3><p id=\"fs-id1167836293187\">We used the equation \\(y=2x-3\\) and its graph as we developed the vertical line test. We said that the relation defined by the equation \\(y=2x-3\\) is a function.<\/p><p id=\"fs-id1167833020798\">We can write this as in function notation as \\(f\\left(x\\right)=2x-3.\\) It still means the same thing. The graph of the function is the graph of all ordered pairs \\(\\left(x,y\\right)\\) where \\(y=f\\left(x\\right).\\) So we can write the ordered pairs as \\(\\left(x,f\\left(x\\right)\\right).\\) It looks different but the graph will be the same.<\/p><p id=\"fs-id1167836685520\">Compare the graph of \\(y=2x-3\\) previously shown in <a href=\"#CNX_IntAlg_Figure_03_06_001\" class=\"autogenerated-content\">(Figure)<\/a> with the graph of \\(f\\left(x\\right)=2x-3\\) shown in <a href=\"#CNX_IntAlg_Figure_03_06_007\" class=\"autogenerated-content\">(Figure)<\/a>. Nothing has changed but the notation.<\/p><div class=\"bc-figure figure\" id=\"CNX_IntAlg_Figure_03_06_007\"><span data-type=\"media\" id=\"fs-id1167836415144\" data-alt=\"This figure has a graph next to a table. The graph has a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled f of x equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label f of x equals2 x minus 3. The second row is a header row with the headers x, f of x, and (x, f of x). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_007_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. The graph has a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled f of x equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label f of x equals2 x minus 3. The second row is a header row with the headers x, f of x, and (x, f of x). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><\/span><\/div><div data-type=\"note\" id=\"fs-id1167829598148\"><div data-type=\"title\">Graph of a Function<\/div><p id=\"fs-id1167836692382\">The graph of a function is the graph of all its ordered pairs, \\(\\left(x,y\\right)\\) or using function notation, \\(\\left(x,f\\left(x\\right)\\right)\\) where \\(y=f\\left(x\\right).\\)<\/p><div data-type=\"equation\" id=\"fs-id1167829719082\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill f&amp; &amp; &amp; \\text{name of function}\\hfill \\\\ \\hfill x&amp; &amp; &amp; x\\text{-coordinate of the ordered pair}\\hfill \\\\ \\hfill f\\left(x\\right)&amp; &amp; &amp; y\\text{-coordinate of the ordered pair}\\hfill \\end{array}\\)<\/div><\/div><p id=\"fs-id1167836321563\">As we move forward in our study, it is helpful to be familiar with the graphs of several basic functions and be able to identify them.<\/p><p id=\"fs-id1167836665565\">Through our earlier work, we are familiar with the graphs of linear equations. The process we used to decide if \\(y=2x-3\\) is a function would apply to all linear equations. All non-vertical linear equations are functions. Vertical lines are not functions as the <em data-effect=\"italics\">x<\/em>-value has infinitely many <em data-effect=\"italics\">y<\/em>-values.<\/p><p id=\"fs-id1167836480334\">We wrote linear equations in several forms, but it will be most helpful for us here to use the slope-intercept form of the linear equation. The slope-intercept form of a linear equation is \\(y=mx+b.\\) In function notation, this linear function becomes \\(f\\left(x\\right)=mx+b\\) where <em data-effect=\"italics\">m<\/em> is the slope of the line and <em data-effect=\"italics\">b<\/em> is the <em data-effect=\"italics\">y<\/em>-intercept.<\/p><p>The domain is the set of all real numbers, and the range is also the set of all real numbers.<\/p><div data-type=\"note\" id=\"fs-id1167833049966\"><div data-type=\"title\">Linear Function<\/div><span data-type=\"media\" id=\"fs-id1167829790631\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_008_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/div><p id=\"fs-id1167836755080\">We will use the graphing techniques we used earlier, to graph the basic functions.<\/p><div data-type=\"example\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833056074\"><div data-type=\"problem\" id=\"fs-id1167836513618\"><p id=\"fs-id1167836612024\">Graph: \\(f\\left(x\\right)=-2x-4.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836546655\"><table id=\"fs-id1167836688758\" class=\"unnumbered unstyled\" summary=\"We recognize f of x equalsnegative 2 x minus 4 as a linear function. Find the slope and y-intercept. m equalsnegative 2. b equalsnegative 4. Graph using the slope intercept. The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 4), and (negative 1, negative 2).\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{4.5em}{0ex}}f\\left(x\\right)=-2x-4\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">We recognize this as a linear function.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Find the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td><td data-valign=\"top\" data-align=\"left\">\\(\\phantom{\\rule{5.5em}{0ex}}m=-2\\)<div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{5.65em}{0ex}}b=-4\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Graph using the slope intercept.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829746004\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_009a_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829754438\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836406766\"><div data-type=\"problem\" id=\"fs-id1167836601239\"><p id=\"fs-id1167833051555\">Graph: \\(f\\left(x\\right)=-3x-1\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836660083\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" data-alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (1, negative 4), (0, negative 1), and (negative 1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_301_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (1, negative 4), (0, negative 1), and (negative 1, 2).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833128828\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167824781336\"><div data-type=\"problem\"><p id=\"fs-id1167836406990\">Graph: \\(f\\left(x\\right)=-4x-5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829719238\"><p id=\"fs-id1167832925581\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833328995\" data-alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 3), (0, negative 5), and (negative 1, negative 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_302_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 3), (0, negative 5), and (negative 1, negative 1).\"><\/span><\/div><\/div><\/div><p id=\"fs-id1167833054733\">The next function whose graph we will look at is called the constant function and its equation is of the form \\(f\\left(x\\right)=b,\\) where <em data-effect=\"italics\">b<\/em> is any real number. If we replace the \\(f\\left(x\\right)\\) with y, we get \\(y=b.\\) We recognize this as the horizontal line whose <em data-effect=\"italics\">y<\/em>-intercept is <em data-effect=\"italics\">b<\/em>. The graph of the function \\(f\\left(x\\right)=b,\\) is also the horizontal line whose <em data-effect=\"italics\">y<\/em>-intercept is <em data-effect=\"italics\">b<\/em>.<\/p><p id=\"fs-id1167836602424\">Notice that for any real number we put in the function, the function value will be <em data-effect=\"italics\">b<\/em>. This tells us the range has only one value, <em data-effect=\"italics\">b<\/em>.<\/p><div data-type=\"note\" id=\"fs-id1167836494179\"><div data-type=\"title\">Constant Function<\/div><span data-type=\"media\" id=\"fs-id1167836684877\" data-alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_010_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><\/span><\/div><div data-type=\"example\" id=\"fs-id1167833142741\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836525068\"><div data-type=\"problem\" id=\"fs-id1167824764495\"><p id=\"fs-id1167836433572\">Graph: \\(f\\left(x\\right)=4.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833060151\"><table id=\"fs-id1167836560655\" class=\"unnumbered unstyled\" summary=\"We recognize f of x equals4 as a constant function. The graph will be a horizontal line through (0, 4). The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The line goes through the points (negative 2, 4), (0, 4), and (1, 4).\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"center\">\\(f\\left(x\\right)=4\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">We recognize this as a constant function.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">The graph will be a horizontal line through \\(\\left(0,4\\right).\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836514168\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_011a_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836481166\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167824736254\"><div data-type=\"problem\" id=\"fs-id1167836557139\"><p id=\"fs-id1167824764946\">Graph: \\(f\\left(x\\right)=-2.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829878652\"><p id=\"fs-id1167836399311\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829851276\" data-alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_303_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836558185\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836487148\"><div data-type=\"problem\" id=\"fs-id1167836552606\"><p id=\"fs-id1167825091690\">Graph: \\(f\\left(x\\right)=3.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836501611\"><p id=\"fs-id1167833053412\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836409269\" data-alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3), (1, 3), and (2, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_304_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3), (1, 3), and (2, 3).\"><\/span><\/div><\/div><\/div><p id=\"fs-id1167836528178\">The identity function, \\(f\\left(x\\right)=x\\) is a special case of the linear function. If we write it in linear function form, \\(f\\left(x\\right)=1x+0,\\) we see the slope is 1 and the <em data-effect=\"italics\">y<\/em>-intercept is 0.<\/p><div data-type=\"note\" id=\"fs-id1167824674086\"><div data-type=\"title\">Identity Function<\/div><span data-type=\"media\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_012_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/div><p id=\"fs-id1167826171267\">The next function we will look at is not a linear function. So the graph will not be a line. The only method we have to graph this function is point plotting. Because this is an unfamiliar function, we make sure to choose several positive and negative values as well as 0 for our x-values.<\/p><div data-type=\"example\" id=\"fs-id1167836683384\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836646170\"><div data-type=\"problem\" id=\"fs-id1167833345125\"><p id=\"fs-id1167836650008\">Graph: \\(f\\left(x\\right)={x}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833396805\"><p id=\"fs-id1167833339306\">We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart as shown.<\/p><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167836295348\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 3, 9), (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), (2, 4), and (3, 9). The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx squared, and (x, f of x). The second row has the coordinates negative 3, 9, and (negative 3, 9). The third row has the coordinates negative 2, 4, and (negative 2, 4). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 4, and (2, 4). The seventh row has the coordinates 3, 9, and (3, 9).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_013_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 3, 9), (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), (2, 4), and (3, 9). The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx squared, and (x, f of x). The second row has the coordinates negative 3, 9, and (negative 3, 9). The third row has the coordinates negative 2, 4, and (negative 2, 4). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 4, and (2, 4). The seventh row has the coordinates 3, 9, and (3, 9).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836530814\"><div data-type=\"problem\"><p>Graph: \\(f\\left(x\\right)={x}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836768461\"><p id=\"fs-id1167836731140\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833139707\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_305_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829930524\"><div data-type=\"problem\" id=\"fs-id1167829695062\"><p id=\"fs-id1167833051245\">\\(f\\left(x\\right)=\\text{\u2212}{x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833237691\"><p id=\"fs-id1167836288172\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833197255\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, negative 4), (negative 1, negative 1), (0, 0), (1, negative 1), and (2, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_306_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, negative 4), (negative 1, negative 1), (0, 0), (1, negative 1), and (2, negative 4).\"><\/span><\/div><\/div><\/div><p id=\"fs-id1167829783193\">Looking at the result in <a href=\"#fs-id1167836683384\" class=\"autogenerated-content\">(Figure)<\/a>, we can summarize the features of the square function. We call this graph a parabola. As we consider the domain, notice any real number can be used as an <em data-effect=\"italics\">x<\/em>-value. The domain is all real numbers.<\/p><p>The range is not all real numbers. Notice the graph consists of values of <em data-effect=\"italics\">y<\/em> never go below zero. This makes sense as the square of any number cannot be negative. So, the range of the square function is all non-negative real numbers.<\/p><div data-type=\"note\" id=\"fs-id1167824617137\"><div data-type=\"title\">Square Function<\/div><span data-type=\"media\" id=\"fs-id1167829744925\" data-alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_014_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/div><p>The next function we will look at is also not a linear function so the graph will not be a line. Again we will use point plotting, and make sure to choose several positive and negative values as well as 0 for our <em data-effect=\"italics\">x<\/em>-values.<\/p><div data-type=\"example\" id=\"fs-id1167832966170\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836572855\"><div data-type=\"problem\" id=\"fs-id1167824701409\"><p>Graph: \\(f\\left(x\\right)={x}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829756525\"><p>We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart.<\/p><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167833020710\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8). Next to the graph is a table. The table has 6 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx cubed, and (x, f of x). The second row has the coordinates negative 2, negative 8, and (negative 2, negative 8). The third row has the coordinates negative 1, negative 1, and (negative 1, negative 1). The fourth row has the coordinates 0, 0, and (0, 0). The fifth row has the coordinates 1, 1, and (1, 1). The sixth row has the coordinates 2, 8, and (2, 8).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_015_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8). Next to the graph is a table. The table has 6 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx cubed, and (x, f of x). The second row has the coordinates negative 2, negative 8, and (negative 2, negative 8). The third row has the coordinates negative 1, negative 1, and (negative 1, negative 1). The fourth row has the coordinates 0, 0, and (0, 0). The fifth row has the coordinates 1, 1, and (1, 1). The sixth row has the coordinates 2, 8, and (2, 8).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836553231\"><div data-type=\"problem\" id=\"fs-id1167833060462\"><p id=\"fs-id1167836743450\">Graph: \\(f\\left(x\\right)={x}^{3}.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836519057\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833056490\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_307_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167832982045\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833196697\"><div data-type=\"problem\" id=\"fs-id1167829907663\"><p>Graph: \\(f\\left(x\\right)=\\text{\u2212}{x}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836775118\"><p id=\"fs-id1167829984244\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836434321\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, 8), (negative 1, 1), (0, 0), (1, negative 1), and (2, negative 8).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_308_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, 8), (negative 1, 1), (0, 0), (1, negative 1), and (2, negative 8).\"><\/span><\/div><\/div><\/div><p id=\"fs-id1167836598078\">Looking at the result in <a href=\"#fs-id1167832966170\" class=\"autogenerated-content\">(Figure)<\/a>, we can summarize the features of the cube function. As we consider the domain, notice any real number can be used as an <em data-effect=\"italics\">x<\/em>-value. The domain is all real numbers.<\/p><p id=\"fs-id1167836787693\">The range is all real numbers. This makes sense as the cube of any non-zero number can be positive or negative. So, the range of the cube function is all real numbers.<\/p><div data-type=\"note\" id=\"fs-id1167829687218\"><div data-type=\"title\">Cube Function<\/div><span data-type=\"media\" id=\"fs-id1167836496942\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_016_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/div><p id=\"fs-id1167833023152\">The next function we will look at does not square or cube the input values, but rather takes the square root of those values.<\/p><p id=\"fs-id1167836512756\">Let\u2019s graph the function \\(f\\left(x\\right)=\\sqrt{x}\\) and then summarize the features of the function. Remember, we can only take the square root of non-negative real numbers, so our domain will be the non-negative real numbers.<\/p><div data-type=\"example\" id=\"fs-id1167829930477\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833350001\"><div data-type=\"problem\" id=\"fs-id1167836569057\"><p id=\"fs-id1167833019425\">\\(f\\left(x\\right)=\\sqrt{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833326611\"><p id=\"fs-id1167829921787\">We choose <em data-effect=\"italics\">x<\/em>-values. Since we will be taking the square root, we choose numbers that are perfect squares, to make our work easier. We substitute them in and then create a chart.<\/p><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167829686050\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph is a table. The table has 5 rows and 3 columns. The first row is a header row with the headers x, f of x equalssquare root of x, and (x, f of x). The second row has the coordinates 0, 0, and (0, 0). The third row has the coordinates 1, 1, and (1, 1). The fourth row has the coordinates 4, 2, and (4, 2). The fifth row has the coordinates 9, 3, and (9, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_017_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph is a table. The table has 5 rows and 3 columns. The first row is a header row with the headers x, f of x equalssquare root of x, and (x, f of x). The second row has the coordinates 0, 0, and (0, 0). The third row has the coordinates 1, 1, and (1, 1). The fourth row has the coordinates 4, 2, and (4, 2). The fifth row has the coordinates 9, 3, and (9, 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836341594\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836378266\"><div data-type=\"problem\" id=\"fs-id1167836623811\"><p id=\"fs-id1167836730489\">Graph: \\(f\\left(x\\right)=\\sqrt{x}.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836525446\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1), (4, 2), and (9, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_309_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1), (4, 2), and (9, 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836650089\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836510334\"><div data-type=\"problem\"><p id=\"fs-id1167836602315\">Graph: \\(f\\left(x\\right)=\\text{\u2212}\\sqrt{x}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167830077318\"><p id=\"fs-id1167833139590\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167824733299\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from negative 10 to 0. The curved half-line starts at the point (0, 0) and then goes down and to the right. The curved half line goes through the points (1, negative 1), (4, negative 2), and (9, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_310_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from negative 10 to 0. The curved half-line starts at the point (0, 0) and then goes down and to the right. The curved half line goes through the points (1, negative 1), (4, negative 2), and (9, negative 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836664843\"><div data-type=\"title\">Square Root Function<\/div><span data-type=\"media\" id=\"fs-id1167836292233\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_018_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/div><p id=\"fs-id1167836299963\">Our last basic function is the absolute value function, \\(f\\left(x\\right)=|x|.\\) Keep in mind that the absolute value of a number is its distance from zero. Since we never measure distance as a negative number, we will never get a negative number in the range.<\/p><div data-type=\"example\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836417983\"><div data-type=\"problem\" id=\"fs-id1167836531216\"><p>Graph: \\(f\\left(x\\right)=|x|.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836707251\"><p>We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart.<\/p><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167836614974\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). Next to the graph is a table. The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsabsolute value of x, and (x, f of x). The second row has the coordinates negative 3, 3, and (negative 3, 3). The third row has the coordinates negative 2, 2, and (negative 2, 2). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 2, and (2, 2). The eighth row has the coordinates 3, 3, and (3, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_019_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). Next to the graph is a table. The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsabsolute value of x, and (x, f of x). The second row has the coordinates negative 3, 3, and (negative 3, 3). The third row has the coordinates negative 2, 2, and (negative 2, 2). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 2, and (2, 2). The eighth row has the coordinates 3, 3, and (3, 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833350872\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836441074\"><p id=\"fs-id1167836376954\">Graph: \\(f\\left(x\\right)=|x|.\\)<\/p><\/div><div data-type=\"solution\"><p><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833014880\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_311_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836625638\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833378973\"><div data-type=\"problem\" id=\"fs-id1167836595957\"><p id=\"fs-id1167836349492\">Graph: \\(f\\left(x\\right)=\\text{\u2212}|x|.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167830123030\"><p id=\"fs-id1167836787910\"><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833023118\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The v-shaped line goes through the points (negative 3, negative 3), (negative 2, negative 2), (negative 1, negative 1), (0, 0), (1, negative 1), (2, negative 2), and (3, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_312_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The v-shaped line goes through the points (negative 3, negative 3), (negative 2, negative 2), (negative 1, negative 1), (0, 0), (1, negative 1), (2, negative 2), and (3, negative 3).\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836389848\"><div data-type=\"title\">Absolute Value Function<\/div><span data-type=\"media\" id=\"fs-id1167836335262\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_020_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836386547\"><h3 data-type=\"title\">Read Information from a Graph of a Function<\/h3><p id=\"fs-id1167833022366\">In the sciences and business, data is often collected and then graphed. The graph is analyzed, information is obtained from the graph and then often predictions are made from the data.<\/p><p id=\"fs-id1167836620724\">We will start by reading the domain and range of a function from its graph.<\/p><p id=\"fs-id1167836514287\">Remember the domain is the set of all the <em data-effect=\"italics\">x<\/em>-values in the ordered pairs in the function. To find the domain we look at the graph and find all the values of <em data-effect=\"italics\">x<\/em> that have a corresponding value on the graph. Follow the value <em data-effect=\"italics\">x<\/em> up or down vertically. If you hit the graph of the function then <em data-effect=\"italics\">x<\/em> is in the domain.<\/p><p id=\"fs-id1167825884739\">Remember the range is the set of all the <em data-effect=\"italics\">y<\/em>-values in the ordered pairs in the function. To find the range we look at the graph and find all the values of <em data-effect=\"italics\">y<\/em> that have a corresponding value on the graph. Follow the value <em data-effect=\"italics\">y<\/em> left or right horizontally. If you hit the graph of the function then <em data-effect=\"italics\">y<\/em> is in the range.<\/p><div data-type=\"example\" id=\"fs-id1167829756085\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833047462\"><div data-type=\"problem\" id=\"fs-id1167829688185\"><p id=\"fs-id1167833057048\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p><span data-type=\"media\" id=\"fs-id1167836538244\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 3, negative 1), (1.5, 3), and (3, 1). The interval [negative 3, 3] is marked on the horizontal axis. The interval [negative 1, 3] is marked on the vertical axis.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_021_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 3, negative 1), (1.5, 3), and (3, 1). The interval [negative 3, 3] is marked on the horizontal axis. The interval [negative 1, 3] is marked on the vertical axis.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836513079\"><p id=\"fs-id1167833158804\">To find the domain we look at the graph and find all the values of <em data-effect=\"italics\">x<\/em> that correspond to a point on the graph. The domain is highlighted in red on the graph. The domain is \\(\\left[-3,3\\right].\\)<\/p><p id=\"fs-id1167836611195\">To find the range we look at the graph and find all the values of <em data-effect=\"italics\">y<\/em> that correspond to a point on the graph. The range is highlighted in blue on the graph. The range is \\(\\left[-1,3\\right].\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836529485\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167829790459\"><p id=\"fs-id1167833316764\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p><span data-type=\"media\" id=\"fs-id1167829597137\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 5, negative 4), (0, negative 3), and (1, 2). The interval [negative 5, 1] is marked on the horizontal axis. The interval [negative 4, 2] is marked on the vertical axis.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_022_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 5, negative 4), (0, negative 3), and (1, 2). The interval [negative 5, 1] is marked on the horizontal axis. The interval [negative 4, 2] is marked on the vertical axis.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836525200\"><p id=\"fs-id1167825702858\">The domain is \\(\\left[-5,1\\right].\\) The range is \\(\\left[-4,2\\right].\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829718932\"><div data-type=\"problem\" id=\"fs-id1167836515516\"><p id=\"fs-id1167836613378\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p><span data-type=\"media\" id=\"fs-id1167833128692\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 5. The y-axis runs from negative 6 to 4. The curved line segment goes through the points (negative 2, 1), (0, 3), and (4, negative 5). The interval [negative 2, 4] is marked on the horizontal axis. The interval [negative 5, 3] is marked on the vertical axis.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_023_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 5. The y-axis runs from negative 6 to 4. The curved line segment goes through the points (negative 2, 1), (0, 3), and (4, negative 5). The interval [negative 2, 4] is marked on the horizontal axis. The interval [negative 5, 3] is marked on the vertical axis.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829807801\"><p id=\"fs-id1167836576127\">The domain is \\(\\left[-2,4\\right].\\) The range is \\(\\left[-5,3\\right].\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836515910\">We are now going to read information from the graph that you may see in future math classes.<\/p><div data-type=\"example\" id=\"fs-id1167836731462\" class=\"textbox textbox--examples\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836450768\"><p id=\"fs-id1167836323347\">Use the graph of the function to find the indicated values.<\/p><span data-type=\"media\" id=\"fs-id1167836493218\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_024_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167836377545\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(\\frac{3}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(-\\frac{1}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167836289629\"><p id=\"fs-id1167836507194\"><span class=\"token\">\u24d0<\/span> When \\(x=0,\\) the function crosses the <em data-effect=\"italics\">y<\/em>-axis at 0. So, \\(f\\left(0\\right)=0.\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> When \\(x=\\frac{3}{2}\\pi ,\\) the <em data-effect=\"italics\">y<\/em>-value of the function is \\(-1.\\) So, \\(f\\left(\\frac{3}{2}\\pi \\right)=-1.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> When \\(x=-\\frac{1}{2}\\pi ,\\) the <em data-effect=\"italics\">y<\/em>-value of the function is \\(-1.\\) So, \\(f\\left(-\\frac{1}{2}\\pi \\right)=-1.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> The function is 0 at the points, \\(\\left(-2\\pi ,0\\right),\\left(\\text{\u2212}\\pi ,0\\right),\\left(0,0\\right),\\left(\\pi ,0\\right),\\left(2\\pi ,0\\right).\\) The <em data-effect=\"italics\">x<\/em>-values when \\(f\\left(x\\right)=0\\) are \\(-2\\pi ,\\text{\u2212}\\pi ,0,\\pi ,2\\pi .\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> The <em data-effect=\"italics\">x<\/em>-intercepts occur when \\(y=0.\\) So the <em data-effect=\"italics\">x<\/em>-intercepts occur when \\(f\\left(x\\right)=0.\\) The <em data-effect=\"italics\">x<\/em>-intercepts are \\(\\left(-2\\pi ,0\\right),\\left(\\text{\u2212}\\pi ,0\\right),\\left(0,0\\right),\\left(\\pi ,0\\right),\\left(2\\pi ,0\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> The <em data-effect=\"italics\">y<\/em>-intercepts occur when \\(x=0.\\) So the <em data-effect=\"italics\">y<\/em>-intercepts occur at \\(f\\left(0\\right).\\) The <em data-effect=\"italics\">y<\/em>-intercept is \\(\\left(0,0\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> This function has a value when <em data-effect=\"italics\">x<\/em> is from \\(-2\\pi \\) to \\(2\\pi .\\) Therefore, the domain in interval notation is \\(\\left[-2\\pi ,2\\pi \\right].\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> This function values, or <em data-effect=\"italics\">y<\/em>-values go from \\(-1\\) to 1. Therefore, the range, in interval notation, is \\(\\left[-1,1\\right].\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836507624\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829685616\"><div data-type=\"problem\" id=\"fs-id1167836547928\"><p id=\"fs-id1167833007616\">Use the graph of the function to find the indicated values.<\/p><span data-type=\"media\" id=\"fs-id1167836539761\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 2), (negative pi, 0), (negative 1 divided by 2 times pi, negative 2), (0, 0), (1 divided by 2 times pi, 2), (pi, 0), (3 divided by 2 times pi, negative 2), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 2) and (1 divided by 2 times pi, 2) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 2) and (3 divided by 2 times pi, negative 2) are the lowest points on the graph. The line extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_025_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 2), (negative pi, 0), (negative 1 divided by 2 times pi, negative 2), (0, 0), (1 divided by 2 times pi, 2), (pi, 0), (3 divided by 2 times pi, negative 2), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 2) and (1 divided by 2 times pi, 2) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 2) and (3 divided by 2 times pi, negative 2) are the lowest points on the graph. The line extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167836418791\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(\\frac{1}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(-\\frac{3}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167829753187\"><p id=\"fs-id1167836550513\"><span class=\"token\">\u24d0<\/span>\\(f\\left(0\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(f=\\left(\\frac{\\pi }{2}\\right)=2\\)<span class=\"token\">\u24d2<\/span>\\(f=\\left(\\frac{-3\\pi }{2}\\right)=2\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(x\\right)=0\\) for \\(x=-2\\pi ,\\text{\u2212}\\pi ,0,\\pi ,2\\pi \\) <span class=\"token\">\u24d4<\/span> \\(\\left(-2\\pi ,0\\right),\\left(\\text{\u2212}\\pi ,0\\right),\\left(0,0\\right),\\left(\\pi ,0\\right),\\left(2\\pi ,0\\right)\\) <span class=\"token\">\u24d5<\/span> \\(\\left(0,0\\right)\\) <span class=\"token\">\u24d6<\/span> \\(\\left[-2\\pi ,2\\pi \\right]\\) <span class=\"token\">\u24d7<\/span> \\(\\left[-2,2\\right]\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829999559\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836510817\"><div data-type=\"problem\"><p id=\"fs-id1167833240128\">Use the graph of the function to find the indicated values.<\/p><span data-type=\"media\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 1), (negative 3 divided by 2 times pi, 0), (negative pi, negative 1), (negative 1 divided by 2 times pi, 0), (0, 1), (1 divided by 2 times pi, 0), (pi, negative 1), (3 divided by 2 times pi, 0), and (2 times pi, 1). The points (negative 2 times pi, 1), (0, 1), and (2 times pi, 1) are the highest points on the graph. The points (negative pi, negative 1) and (pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_026_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 1), (negative 3 divided by 2 times pi, 0), (negative pi, negative 1), (negative 1 divided by 2 times pi, 0), (0, 1), (1 divided by 2 times pi, 0), (pi, negative 1), (3 divided by 2 times pi, 0), and (2 times pi, 1). The points (negative 2 times pi, 1), (0, 1), and (2 times pi, 1) are the highest points on the graph. The points (negative pi, negative 1) and (pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167836526481\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(\\text{\u2212}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167836378109\"><p id=\"fs-id1167836612647\"><span class=\"token\">\u24d0<\/span>\\(f\\left(0\\right)=1\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(\\pi \\right)=-1\\)<span class=\"token\">\u24d2<\/span>\\(f\\left(\\text{\u2212}\\pi \\right)=-1\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(x\\right)=0\\) for \\(x=-\\frac{3\\pi }{2},-\\frac{\\pi }{2},\\frac{\\pi }{2},\\frac{3\\pi }{2}\\) <span class=\"token\">\u24d4<\/span> \\(\\left(-2\\text{pi},0\\right),\\left(\\text{\u2212pi},0\\right),\\left(0,0\\right),\\left(\\text{pi},0\\right),\\left(2\\text{pi},0\\right)\\) <span class=\"token\">\u24d5<\/span> \\(\\left(0,1\\right)\\) <span class=\"token\">\u24d6<\/span> \\(\\left[-2\\text{pi},2\\text{pi}\\right]\\) <span class=\"token\">\u24d7<\/span> \\(\\left[-1,1\\right]\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"media-2\"><p id=\"fs-id1167836362135\">Access this online resource for additional instruction and practice with graphs of functions.<\/p><ul id=\"fs-id1167836509634\" data-display=\"block\"><li><a href=\"https:\/\/openstax.org\/l\/37domainrange\">Find Domain and Range<\/a><\/li><\/ul><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836597228\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167833036726\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">Vertical Line Test<\/strong><ul id=\"fs-id1167836612581\" data-bullet-style=\"bullet\"><li>A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point.<\/li><li>If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/li><\/ul><\/li><li><strong data-effect=\"bold\">Graph of a Function<\/strong><ul id=\"fs-id1167836386300\" data-bullet-style=\"bullet\"><li>The graph of a function is the graph of all its ordered pairs, \\(\\left(x,y\\right)\\) or using function notation, \\(\\left(x,f\\left(x\\right)\\right)\\) where \\(y=f\\left(x\\right).\\)<div data-type=\"newline\"><br><\/div> <div data-type=\"equation\" id=\"fs-id1167836706023\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill f&amp; &amp; &amp; \\text{name of function}\\hfill \\\\ \\hfill x&amp; &amp; &amp; x\\text{-coordinate of the ordered pair}\\hfill \\\\ \\hfill f\\left(x\\right)&amp; &amp; &amp; y\\text{-coordinate of the ordered pair}\\hfill \\end{array}\\)<\/div><\/li><\/ul><\/li><li><strong data-effect=\"bold\">Linear Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833240439\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_027_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Constant Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836699152\" data-alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_028_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Identity Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167826129331\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_029_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Square Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836612513\" data-alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_030_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Cube Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833380845\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_031_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Square Root Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833245744\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_032_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/li><li><strong data-effect=\"bold\">Absolute Value Function<\/strong><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836602267\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_033_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><\/span><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836310305\"><h3 data-type=\"title\">Section Exercises<\/h3><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167836300671\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167829833896\"><strong data-effect=\"bold\">Use the Vertical Line Test<\/strong><\/p><p>In the following exercises, determine whether each graph is the graph of a function.<\/p><div data-type=\"exercise\" id=\"fs-id1167833256037\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829644953\"><p id=\"fs-id1167836620309\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832998983\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 3, 0), (3, 0), (0, negative 3), and (0, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_201_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 3, 0), (3, 0), (0, negative 3), and (0, 3).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836315012\" data-alt=\"The figure has a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (1, 3), (0, 2), (1, 3), and (2, 6).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_202_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (1, 3), (0, 2), (1, 3), and (2, 6).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836410565\"><p id=\"fs-id1167836361332\"><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833059978\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829579698\"><p id=\"fs-id1167829720945\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836341027\" data-alt=\"The figure has an s-shaped curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The s-shaped curved line goes through the points (negative 1, 1), (0, 0), and (1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_203_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an s-shaped curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The s-shaped curved line goes through the points (negative 1, 1), (0, 0), and (1, 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829713245\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 4, 0), (4, 0), (0, negative 4), and (0, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_204_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 4, 0), (4, 0), (0, negative 4), and (0, 4).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836628720\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836529276\"><p id=\"fs-id1167836621660\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836662706\" data-alt=\"The figure has a parabola opening right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (negative 2, 2), and (2, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_205_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (negative 2, 2), and (2, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833379683\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_206_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836665260\"><p><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836362052\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836612768\"><p id=\"fs-id1167829589830\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836322912\" data-alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 2, 0), (negative 4, 5), and (negative 4, negative 5). The curved line on the right goes through the points (2, 0), (4, 5), and (4, negative 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_207_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 2, 0), (negative 4, 5), and (negative 4, negative 5). The curved line on the right goes through the points (2, 0), (4, 5), and (4, negative 5).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" data-alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, 2) and goes to the right. The line goes through the points (1, 3), (2, 4), (1, 1), and (2, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_208_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, 2) and goes to the right. The line goes through the points (1, 3), (2, 4), (1, 1), and (2, 0).\"><\/span><\/div><\/div><p id=\"fs-id1167833377170\"><strong data-effect=\"bold\">Identify Graphs of Basic Functions<\/strong><\/p><p>In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range. Write the domain and range in interval notation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836665073\"><div data-type=\"problem\" id=\"fs-id1167836477133\"><p id=\"fs-id1167836330144\">\\(f\\left(x\\right)=3x+4\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836296139\"><p id=\"fs-id1167829849369\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836356672\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, negative 2), (negative 1, 1), and (0, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_313_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, negative 2), (negative 1, 1), and (0, 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829936987\"><div data-type=\"problem\" id=\"fs-id1167832945825\"><p id=\"fs-id1167833058860\">\\(f\\left(x\\right)=2x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824736142\"><div data-type=\"problem\" id=\"fs-id1167824649348\"><p id=\"fs-id1167836560312\">\\(f\\left(x\\right)=\\text{\u2212}x-2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833350800\"><p id=\"fs-id1167836299759\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836530065\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 2), and (2, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_315_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 2), and (2, negative 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829624127\"><div data-type=\"problem\" id=\"fs-id1167833082143\"><p id=\"fs-id1167836362620\">\\(f\\left(x\\right)=-4x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836694784\"><div data-type=\"problem\" id=\"fs-id1167836312665\"><p id=\"fs-id1167836615461\">\\(f\\left(x\\right)=-2x+2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826025216\"><p id=\"fs-id1167833269954\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836717417\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 2), (negative 1, 0), and (0, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_317_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 2), (negative 1, 0), and (0, negative 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836418803\"><div data-type=\"problem\" id=\"fs-id1167833128282\"><p id=\"fs-id1167829931393\">\\(f\\left(x\\right)=-3x+3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833128830\"><div data-type=\"problem\" id=\"fs-id1167829880227\"><p id=\"fs-id1167836732495\">\\(f\\left(x\\right)=\\frac{1}{2}x+1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836516066\"><p id=\"fs-id1167836628122\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832936324\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, 1), and (2, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_319_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, 1), and (2, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824658727\"><div data-type=\"problem\" id=\"fs-id1167836361338\"><p id=\"fs-id1167833256412\">\\(f\\left(x\\right)=\\frac{2}{3}x-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836544127\"><div data-type=\"problem\" id=\"fs-id1167836319404\"><p id=\"fs-id1167824732917\">\\(f\\left(x\\right)=5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836407696\"><p id=\"fs-id1167836649918\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829878394\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 5), and (0, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_321_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 5), and (0, 5).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:{5}<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836429353\"><div data-type=\"problem\" id=\"fs-id1167836310954\"><p id=\"fs-id1167836282751\">\\(f\\left(x\\right)=2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829745945\"><div data-type=\"problem\" id=\"fs-id1167836520136\"><p id=\"fs-id1167836546248\">\\(f\\left(x\\right)=-3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836510430\"><p id=\"fs-id1167836706859\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836513491\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, negative 3), (1, negative 3), and (2, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_323_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, negative 3), (1, negative 3), and (2, negative 3).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R: \\(\\left\\{-3\\right\\}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829719517\"><div data-type=\"problem\" id=\"fs-id1167829807022\"><p id=\"fs-id1167836635569\">\\(f\\left(x\\right)=-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836731888\"><div data-type=\"problem\" id=\"fs-id1167836685446\"><p id=\"fs-id1167836712402\">\\(f\\left(x\\right)=2x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836545379\"><p id=\"fs-id1167836550226\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836447279\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 0), (2, 4), and (negative 2, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_325_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 0), (2, 4), and (negative 2, negative 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836626104\"><div data-type=\"problem\" id=\"fs-id1167836662613\"><p id=\"fs-id1167836552854\">\\(f\\left(x\\right)=3x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836621812\"><div data-type=\"problem\" id=\"fs-id1167833310489\"><p id=\"fs-id1167833135075\">\\(f\\left(x\\right)=-2x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836330168\"><p id=\"fs-id1167836539196\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836691433\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 0), (1, negative 2), and (negative 1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_327_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 0), (1, negative 2), and (negative 1, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829599925\"><div data-type=\"problem\" id=\"fs-id1167829851557\"><p id=\"fs-id1167826177592\">\\(f\\left(x\\right)=-3x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836698477\"><div data-type=\"problem\" id=\"fs-id1167836625081\"><p id=\"fs-id1167836533854\">\\(f\\left(x\\right)=3{x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836296574\"><p id=\"fs-id1167829830462\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829719707\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_329_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:[0,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836481202\"><div data-type=\"problem\" id=\"fs-id1167836613666\"><p id=\"fs-id1167833021907\">\\(f\\left(x\\right)=2{x}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836722566\"><div data-type=\"problem\" id=\"fs-id1167836730654\"><p id=\"fs-id1167836361907\">\\(f\\left(x\\right)=-3{x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832976376\"><p id=\"fs-id1167836522879\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833186678\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 10 to 2. The parabola goes through the points (negative 1, negative 3), (0, 0), and (1, negative 3). The highest point on the graph is (0, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_331_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 10 to 2. The parabola goes through the points (negative 1, negative 3), (0, 0), and (1, negative 3). The highest point on the graph is (0, 0).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:(-\u221e,0]<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836549919\"><div data-type=\"problem\" id=\"fs-id1167836326911\"><p id=\"fs-id1167836492164\">\\(f\\left(x\\right)=-2{x}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836321873\"><div data-type=\"problem\"><p id=\"fs-id1167836319029\">\\(f\\left(x\\right)=\\frac{1}{2}{x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824765152\"><p id=\"fs-id1167836510523\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829749853\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 4, 8), (negative 2, 2), (0, 0), (2, 2), and (4, 8). The lowest point on the graph is (0, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_333_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 4, 8), (negative 2, 2), (0, 0), (2, 2), and (4, 8). The lowest point on the graph is (0, 0).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:[-\u221e,0)<\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167824732033\"><p id=\"fs-id1167836329509\">\\(f\\left(x\\right)=\\frac{1}{3}{x}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167826169717\"><p id=\"fs-id1167829878789\">\\(f\\left(x\\right)={x}^{2}-1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836362657\"><p id=\"fs-id1167836556201\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833025407\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 3), (negative 1, 0), (0, negative 1), (1, 0), and (2, 3). The lowest point on the graph is (0, negative 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_335_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 3), (negative 1, 0), (0, negative 1), (1, 0), and (2, 3). The lowest point on the graph is (0, negative 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:[\\(-1,\\) \u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836662424\"><div data-type=\"problem\" id=\"fs-id1167833082497\"><p id=\"fs-id1167829689678\">\\(f\\left(x\\right)={x}^{2}+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829650694\"><div data-type=\"problem\" id=\"fs-id1167836791239\"><p>\\(f\\left(x\\right)=-2{x}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829695009\"><p id=\"fs-id1167833346213\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833051204\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_337_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836693431\"><div data-type=\"problem\" id=\"fs-id1167836602619\"><p id=\"fs-id1167836526432\">\\(f\\left(x\\right)=2{x}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836341365\"><div data-type=\"problem\" id=\"fs-id1167833056424\"><p id=\"fs-id1167829750112\">\\(f\\left(x\\right)={x}^{3}+2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836717043\"><p id=\"fs-id1167824584281\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829688798\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_339_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836415699\"><div data-type=\"problem\" id=\"fs-id1167836699822\"><p id=\"fs-id1167836701108\">\\(f\\left(x\\right)={x}^{3}-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836481043\"><div data-type=\"problem\" id=\"fs-id1167826132631\"><p id=\"fs-id1167836375975\">\\(f\\left(x\\right)=2\\sqrt{x}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833142040\"><p id=\"fs-id1167836310146\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836510096\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (0, 0) and goes through the points (1, 2) and (4, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_341_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (0, 0) and goes through the points (1, 2) and (4, 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:[0,\u221e), R:[0,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833054162\"><div data-type=\"problem\" id=\"fs-id1167836521944\"><p id=\"fs-id1167836322682\">\\(f\\left(x\\right)=-2\\sqrt{x}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836510676\"><div data-type=\"problem\" id=\"fs-id1167836624651\"><p id=\"fs-id1167836455857\">\\(f\\left(x\\right)=\\sqrt{x-1}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826170204\"><p id=\"fs-id1167836514110\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836511382\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_343_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:[1,\u221e), R:[0,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829589762\"><div data-type=\"problem\" id=\"fs-id1167836368147\"><p id=\"fs-id1167836628623\">\\(f\\left(x\\right)=\\sqrt{x+1}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829923887\"><div data-type=\"problem\" id=\"fs-id1167824766922\"><p id=\"fs-id1167836409493\">\\(f\\left(x\\right)=3|x|\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833186644\"><p><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836774098\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 0). The line goes through the points (negative 1, 3) and (1, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_345_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 0). The line goes through the points (negative 1, 3) and (1, 3).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:[ \\(-1,\\) \u221e), R:[\u2212\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829789446\"><div data-type=\"problem\" id=\"fs-id1167833397067\"><p id=\"fs-id1167836556358\">\\(f\\left(x\\right)=-2|x|\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836393413\"><div data-type=\"problem\" id=\"fs-id1167829899539\"><p id=\"fs-id1167829936852\">\\(f\\left(x\\right)=|x|+1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836608457\"><p id=\"fs-id1167836550967\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833024700\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_347_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:[1,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836601960\"><div data-type=\"problem\" id=\"fs-id1167836608052\"><p id=\"fs-id1167829712186\">\\(f\\left(x\\right)=|x|-1\\)<\/p><\/div><\/div><p id=\"fs-id1167836686005\"><strong data-effect=\"bold\">Read Information from a Graph of a Function<\/strong><\/p><p id=\"fs-id1167836579171\">In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836580012\"><div data-type=\"problem\" id=\"fs-id1167836524810\"><span data-type=\"media\" id=\"fs-id1167832999715\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 8. The half-line starts at the point (2, 0) and goes through the points (3, 1) and (6, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_209_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 8. The half-line starts at the point (2, 0) and goes through the points (3, 1) and (6, 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836524162\"><p>D: [2,\u221e), R: [0,\u221e)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836442468\"><div data-type=\"problem\" id=\"fs-id1167829624940\"><span data-type=\"media\" id=\"fs-id1167836285461\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_210_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836692203\"><div data-type=\"problem\" id=\"fs-id1167836504168\"><span data-type=\"media\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from 0 to 12. The vertex is at the point (0, 4). The line goes through the points (negative 2, 6) and (2, 6).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_211_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from 0 to 12. The vertex is at the point (0, 4). The line goes through the points (negative 2, 6) and (2, 6).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836293141\"><p id=\"fs-id1167824590509\">D: (-\u221e,\u221e), R: [4,\u221e)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836361313\"><div data-type=\"problem\" id=\"fs-id1167836363597\"><span data-type=\"media\" id=\"fs-id1167829717427\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The vertex is at the point (0, negative 1). The line goes through the points (negative 1, 0) and (1, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_212_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The vertex is at the point (0, negative 1). The line goes through the points (negative 1, 0) and (1, 0).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836609509\"><div data-type=\"problem\" id=\"fs-id1167836557691\"><span data-type=\"media\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_213_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836688268\"><p id=\"fs-id1167836574099\">D: \\(\\left[-2,2\\right],\\) R: [0, 2]<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833007602\"><div data-type=\"problem\" id=\"fs-id1167829684137\"><span data-type=\"media\" id=\"fs-id1167836545772\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The curved line segment starts at the point (negative 3, 3). The line goes through the point (0, 6) and ends at the point (3, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_214_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The curved line segment starts at the point (negative 3, 3). The line goes through the point (0, 6) and ends at the point (3, 3).\"><\/span><\/div><\/div><p>In the following exercises, use the graph of the function to find the indicated values.<\/p><div data-type=\"exercise\" id=\"fs-id1167829831353\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829590096\"><span data-type=\"media\" id=\"fs-id1167836570194\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, negative 1), (negative pi, 0), (negative 1 divided by 2 times pi, 1), (0, 0), (1 divided by 2 times pi, negative 1), (pi, 0), (3 divided by 2 times pi, 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, negative 1) and (1 divided by 2 times pi, negative 1) are the lowest points on the graph. The points (negative 1 divided by 2 times pi, 1) and (3 divided by 2 times pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_215_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, negative 1), (negative pi, 0), (negative 1 divided by 2 times pi, 1), (0, 0), (1 divided by 2 times pi, negative 1), (pi, 0), (3 divided by 2 times pi, 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, negative 1) and (1 divided by 2 times pi, negative 1) are the lowest points on the graph. The points (negative 1 divided by 2 times pi, 1) and (3 divided by 2 times pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167836645558\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(\\frac{1}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(-\\frac{3}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167829712368\"><p id=\"fs-id1167836441031\"><span class=\"token\">\u24d0<\/span>\\(f\\left(0\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(\\left(\\text{pi}\\text{\/}2\\right)=-1\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(f\\left(-3\\text{pi}\\text{\/}2\\right)=-1\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(x\\right)=0\\) for \\(x=-2\\text{pi},\\text{\u2212}\\text{pi},0,\\text{pi},2\\text{pi}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> \\(\\left(-2\\text{pi},0\\right),\\left(\\text{\u2212}\\text{pi},0\\right),\\) \\(\\left(0,0\\right),\\left(\\text{pi},0\\right),\\left(2\\text{pi},0\\right)\\) \\(\\left(f\\right)\\left(0,0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d6<\/span> \\(\\left[-2\\text{pi},2\\text{pi}\\right]\\) <span class=\"token\">\u24d7<\/span> \\(\\left[-1,1\\right]\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832950981\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829849533\"><span data-type=\"media\" id=\"fs-id1167836626610\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, negative 1), (negative 3 divided by 2 times pi, 0), (negative pi, 1), (negative 1 divided by 2 times pi, 0), (0, negative 1), (1 divided by 2 times pi, 0), (pi, 1), (3 divided by 2 times pi, 0), and (2 times pi, negative 1). The points (negative 2 times pi, negative 1) and (2 times pi, negative 1) are the lowest points on the graph. The points (negative pi, 1) and (pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_216_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, negative 1), (negative 3 divided by 2 times pi, 0), (negative pi, 1), (negative 1 divided by 2 times pi, 0), (0, negative 1), (1 divided by 2 times pi, 0), (pi, 1), (3 divided by 2 times pi, 0), and (2 times pi, negative 1). The points (negative 2 times pi, negative 1) and (2 times pi, negative 1) are the lowest points on the graph. The points (negative pi, 1) and (pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167829696672\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(\\text{\u2212}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836573407\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836432065\"><span data-type=\"media\" data-alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 3, 2). The line goes through the point (0, 5) and ends at the point (3, 2). The point (0, 5) is the highest point on the graph. The points (negative 3, 2) and (3, 2) are the lowest points on the graph.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_217_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 3, 2). The line goes through the point (0, 5) and ends at the point (3, 2). The point (0, 5) is the highest point on the graph. The points (negative 3, 2) and (3, 2) are the lowest points on the graph.\"><\/span><p id=\"fs-id1167836609689\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find: \\(f\\left(-3\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find: \\(f\\left(3\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167836544041\"><p id=\"fs-id1167829714553\"><span class=\"token\">\u24d0<\/span>\\(f\\left(0\\right)=-6\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(-3\\right)=3\\)<span class=\"token\">\u24d2<\/span>\\(f\\left(3\\right)=3\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(x\\right)=0\\) for no <em data-effect=\"italics\">x<\/em> <span class=\"token\">\u24d4<\/span> none <span class=\"token\">\u24d5<\/span> \\(y=6\\) <span class=\"token\">\u24d6<\/span> \\(\\left[-3,3\\right]\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d7<\/span> \\(\\left[-3,6\\right]\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829859771\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833057178\"><span data-type=\"media\" id=\"fs-id1167836525312\" data-alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 4, 0). The line goes through the point (0, 4) and ends at the point (4, 0). The point (0, 4) is the highest point on the graph. The points (negative 4, 0) and (4, 0) are the lowest points on the graph.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_218_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 4, 0). The line goes through the point (0, 4) and ends at the point (4, 0). The point (0, 4) is the highest point on the graph. The points (negative 4, 0) and (4, 0) are the lowest points on the graph.\"><\/span><p id=\"fs-id1167836409782\"><span class=\"token\">\u24d0<\/span> Find: \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation<\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836602786\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167836629192\"><div data-type=\"problem\" id=\"fs-id1167829599508\"><p id=\"fs-id1167833060329\">Explain in your own words how to find the domain from a graph.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830004585\"><div data-type=\"problem\" id=\"fs-id1167836613527\"><p id=\"fs-id1167832977072\">Explain in your own words how to find the range from a graph.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836790091\"><div data-type=\"problem\" id=\"fs-id1167836514007\"><p id=\"fs-id1167833057205\">Explain in your own words how to use the vertical line test.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833381224\"><div data-type=\"problem\" id=\"fs-id1167833049694\"><p id=\"fs-id1167829849522\">Draw a sketch of the square and cube functions. What are the similarities and differences in the graphs?<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167833057322\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1167829599017\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1167830077412\" data-alt=\"The figure shows a table with four rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cuse the vertical line test\u201d, \u201cidentify graphs of basic functions\u201d, and \u201cread information from a graph\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_219_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with four rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cuse the vertical line test\u201d, \u201cidentify graphs of basic functions\u201d, and \u201cread information from a graph\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved\"><\/span><p id=\"fs-id1167836729385\"><span class=\"token\">\u24d1<\/span> After reviewing this checklist, what will you do to become confident for all objectives?<\/p><\/div><\/div><div class=\"review-exercises\" data-depth=\"1\" id=\"fs-id1167836524742\"><h3 data-type=\"title\">Chapter Review Exercises<\/h3><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824674139\"><h4 data-type=\"title\"><a href=\"\/contents\/26e8f94c-1f76-46ec-8e6c-344f06971cf5\" class=\"target-chapter\">Graph Linear Equations in Two Variables<\/a><\/h4><p id=\"fs-id1167836689070\"><strong data-effect=\"bold\">Plot Points in a Rectangular Coordinate System<\/strong><\/p><p id=\"fs-id1167833059130\">In the following exercises, plot each point in a rectangular coordinate system.<\/p><div data-type=\"exercise\" id=\"fs-id1167836560058\"><div data-type=\"problem\" id=\"fs-id1167836560060\"><p id=\"fs-id1167829595121\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\left(-1,-5\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(-3,4\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(2,-3\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(1,\\frac{5}{2}\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836300056\"><span data-type=\"media\" id=\"fs-id1167829621293\" data-alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_349_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.\"><\/span><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167833329338\"><p id=\"fs-id1167829785790\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\left(-2,0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(0,-4\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(0,5\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(3,0\\right)\\)<\/div><\/div><p id=\"fs-id1167836408579\">In the following exercises, determine which ordered pairs are solutions to the given equations.<\/p><div data-type=\"exercise\" id=\"fs-id1167836728880\"><div data-type=\"problem\" id=\"fs-id1167833271954\"><p id=\"fs-id1167833271956\">\\(5x+y=10;\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\left(5,1\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(2,0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(4,-10\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833020246\"><p id=\"fs-id1167833020249\"><span class=\"token\">\u24d1<\/span>, <span class=\"token\">\u24d2<\/span><\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829644642\"><div data-type=\"problem\" id=\"fs-id1167836549257\"><p id=\"fs-id1167836614945\">\\(y=6x-2;\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\left(1,4\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(\\frac{1}{3},0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(6,-2\\right)\\)<\/div><\/div><p id=\"fs-id1167836667122\"><strong data-effect=\"bold\">Graph a Linear Equation by Plotting Points<\/strong><\/p><p id=\"fs-id1167829785046\">In the following exercises, graph by plotting points.<\/p><div data-type=\"exercise\" id=\"fs-id1167836423872\"><div data-type=\"problem\" id=\"fs-id1167836523530\"><p id=\"fs-id1167836523532\">\\(y=4x-3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829628246\"><span data-type=\"media\" id=\"fs-id1167829850431\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_351_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833326537\"><div data-type=\"problem\" id=\"fs-id1167836686054\"><p id=\"fs-id1167836686056\">\\(y=-3x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829859281\"><div data-type=\"problem\" id=\"fs-id1167829859283\"><p id=\"fs-id1167824648946\">\\(y=\\frac{1}{2}x+3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829890835\"><span data-type=\"media\" id=\"fs-id1167833138261\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_353_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836624857\"><div data-type=\"problem\" id=\"fs-id1167836624859\"><p id=\"fs-id1167833378492\">\\(y=-\\frac{4}{5}x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826169944\"><div data-type=\"problem\" id=\"fs-id1167829919797\"><p id=\"fs-id1167833379178\">\\(x-y=6\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836495112\"><span data-type=\"media\" id=\"fs-id1167833208030\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_355_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836705576\"><div data-type=\"problem\" id=\"fs-id1167836705579\"><p id=\"fs-id1167836529723\">\\(2x+y=7\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829688321\"><div data-type=\"problem\" id=\"fs-id1167836689329\"><p id=\"fs-id1167833050658\">\\(3x-2y=6\\)<\/p><\/div><div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167829880330\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_357_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).\"><\/span><\/div><\/div><p id=\"fs-id1167836296637\"><strong data-effect=\"bold\">Graph Vertical and Horizontal lines<\/strong><\/p><p id=\"fs-id1167833019205\">In the following exercises, graph each equation.<\/p><div data-type=\"exercise\" id=\"fs-id1167829861802\"><div data-type=\"problem\" id=\"fs-id1167826131102\"><p id=\"fs-id1167826131104\">\\(y=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836698868\"><div data-type=\"problem\" id=\"fs-id1167832999780\"><p id=\"fs-id1167832999782\">\\(x=3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836628586\"><span data-type=\"media\" id=\"fs-id1167829853783\" data-alt=\"This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_359_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).\"><\/span><\/div><\/div><p id=\"fs-id1167833207874\">In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p><div data-type=\"exercise\" id=\"fs-id1167836611473\"><div data-type=\"problem\" id=\"fs-id1167836429498\"><p id=\"fs-id1167836429500\">\\(y=-2x\\) and \\(y=-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836407159\"><div data-type=\"problem\" id=\"fs-id1167829596805\"><p id=\"fs-id1167829596808\">\\(y=\\frac{4}{3}x\\) and \\(y=\\frac{4}{3}\\)<\/p><\/div><div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167829810794\" data-alt=\"The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_361_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).\"><\/span><\/div><\/div><p id=\"fs-id1167824578489\"><strong data-effect=\"bold\">Find <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em>Intercepts<\/strong><\/p><p id=\"fs-id1167836340022\">In the following exercises, find the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-intercepts.<\/p><div data-type=\"exercise\" id=\"fs-id1167836692041\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836692043\"><span data-type=\"media\" id=\"fs-id1167829840769\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 2), (0, 4), (2, 6), and (4, 8).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_220_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 2), (0, 4), (2, 6), and (4, 8).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829751646\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829751648\"><span data-type=\"media\" id=\"fs-id1167833056929\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 4), (0, 3), (3, 0), and (6, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_221_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 4), (0, 3), (3, 0), and (6, negative 3).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833024082\"><p id=\"fs-id1167836356293\">\\(\\left(0,3\\right)\\left(3,0\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167833369799\">In the following exercises, find the intercepts of each equation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836627814\"><div data-type=\"problem\" id=\"fs-id1167829586489\"><p id=\"fs-id1167836391526\">\\(x-y=-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836514020\"><div data-type=\"problem\" id=\"fs-id1167836514023\"><p id=\"fs-id1167836691368\">\\(x+2y=6\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836729649\"><p id=\"fs-id1167836729651\">\\(\\left(6,0\\right),\\left(0,3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836697400\"><div data-type=\"problem\" id=\"fs-id1167836697402\"><p id=\"fs-id1167833004921\">\\(2x+3y=12\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824737382\"><div data-type=\"problem\" id=\"fs-id1167824737384\"><p id=\"fs-id1167829720692\">\\(y=\\frac{3}{4}x-12\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836386913\"><p id=\"fs-id1167836386915\">\\(\\left(16,0\\right),\\left(0,-12\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836537272\"><div data-type=\"problem\" id=\"fs-id1167833407393\"><p id=\"fs-id1167833407395\">\\(y=3x\\)<\/p><\/div><\/div><p id=\"fs-id1167829595359\"><strong data-effect=\"bold\">Graph a Line Using the Intercepts<\/strong><\/p><p id=\"fs-id1167829906596\">In the following exercises, graph using the intercepts.<\/p><div data-type=\"exercise\" id=\"fs-id1167829877972\"><div data-type=\"problem\" id=\"fs-id1167824737270\"><p>\\(-x+3y=3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833339919\"><span data-type=\"media\" id=\"fs-id1167836559721\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_362_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833057045\"><div data-type=\"problem\" id=\"fs-id1167824731739\"><p id=\"fs-id1167829905654\">\\(x-y=4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824648910\"><div data-type=\"problem\"><p id=\"fs-id1167829586204\">\\(2x-y=5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829851580\"><span data-type=\"media\" id=\"fs-id1167829597299\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_364_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836509101\"><div data-type=\"problem\" id=\"fs-id1167836423881\"><p id=\"fs-id1167836423883\">\\(2x-4y=8\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836626758\"><div data-type=\"problem\" id=\"fs-id1167836507734\"><p id=\"fs-id1167833380731\">\\(y=4x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836513855\"><span data-type=\"media\" id=\"fs-id1167829755848\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_366_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).\"><\/span><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167829740806\"><h4 data-type=\"title\"><a href=\"\/contents\/c7953cb6-51e3-48e7-9969-821f34daec42\" class=\"target-chapter\">Slope of a Line<\/a><\/h4><p id=\"fs-id1167833047231\"><strong data-effect=\"bold\">Find the Slope of a Line<\/strong><\/p><p id=\"fs-id1167836540143\">In the following exercises, find the slope of each line shown.<\/p><div data-type=\"exercise\" id=\"fs-id1167836366545\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836620203\"><span data-type=\"media\" id=\"fs-id1167836620205\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, 0) and (1, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_222_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, 0) and (1, negative 3).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829691193\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829788714\"><span data-type=\"media\" id=\"fs-id1167829788716\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, 0) and (0, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_223_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, 0) and (0, 4).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833175418\"><p id=\"fs-id1167833366014\">1<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836790118\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836790120\"><span data-type=\"media\" id=\"fs-id1167832980890\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, negative 4) and (2, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_224_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, negative 4) and (2, negative 2).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836623132\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836623134\"><span data-type=\"media\" id=\"fs-id1167829905380\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (1, 4) and (5, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_225_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (1, 4) and (5, 2).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829690312\"><p id=\"fs-id1167829690314\">\\(-\\frac{1}{2}\\)<\/p><\/div><\/div><p id=\"fs-id1167836738035\">In the following exercises, find the slope of each line.<\/p><div data-type=\"exercise\" id=\"fs-id1167833086454\"><div data-type=\"problem\" id=\"fs-id1167833036675\"><p id=\"fs-id1167833036677\">\\(y=2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836399770\"><div data-type=\"problem\" id=\"fs-id1167836399772\"><p id=\"fs-id1167832945666\">\\(x=5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836512350\"><p id=\"fs-id1167836356549\">undefined<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836398874\"><div data-type=\"problem\" id=\"fs-id1167836606570\"><p id=\"fs-id1167836606572\">\\(x=-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829578786\"><div data-type=\"problem\"><p>\\(y=-1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836652641\"><p id=\"fs-id1167833224570\">0<\/p><\/div><\/div><p><strong data-effect=\"bold\">Use the Slope Formula to find the Slope of a Line between Two Points<\/strong><\/p><p id=\"fs-id1167829931428\">In the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p><div data-type=\"exercise\" id=\"fs-id1167824734049\"><div data-type=\"problem\" id=\"fs-id1167836664452\"><p id=\"fs-id1167836664454\">\\(\\left(-1,-1\\right),\\left(0,5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836322980\"><div data-type=\"problem\" id=\"fs-id1167836322982\"><p id=\"fs-id1167829790349\">\\(\\left(3.5\\right),\\left(4,-1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833049600\"><p id=\"fs-id1167836455885\">\\(-6\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836738195\"><div data-type=\"problem\" id=\"fs-id1167836738198\"><p id=\"fs-id1167825766169\">\\(\\left(-5,-2\\right),\\left(3,2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836391480\"><div data-type=\"problem\" id=\"fs-id1167836391482\"><p id=\"fs-id1167833310349\">\\(\\left(2,1\\right),\\left(4,6\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836673408\"><p id=\"fs-id1167836673410\">\\(\\frac{5}{2}\\)<\/p><\/div><\/div><p id=\"fs-id1167836387581\"><strong data-effect=\"bold\">Graph a Line Given a Point and the Slope<\/strong><\/p><p id=\"fs-id1167829714127\">In the following exercises, graph each line with the given point and slope.<\/p><div data-type=\"exercise\" id=\"fs-id1167836620933\"><div data-type=\"problem\" id=\"fs-id1167836620935\"><p id=\"fs-id1167829685902\">\\(\\left(2,-2\\right);\\)\\(m=\\frac{5}{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829717719\"><div data-type=\"problem\" id=\"fs-id1167832980872\"><p id=\"fs-id1167832980874\">\\(\\left(-3,4\\right);\\)\\(m=-\\frac{1}{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836408863\"><span data-type=\"media\" id=\"fs-id1167836408866\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_368_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829878927\"><div data-type=\"problem\" id=\"fs-id1167836557400\"><p id=\"fs-id1167836557402\"><em data-effect=\"italics\">x<\/em>-intercept \\(-4;\\)\\(m=3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836536584\"><div data-type=\"problem\" id=\"fs-id1167836536586\"><p id=\"fs-id1167829693217\"><em data-effect=\"italics\">y<\/em>-intercept 1; \\(m=-\\frac{3}{4}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836540579\"><span data-type=\"media\" id=\"fs-id1167836540582\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_370_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).\"><\/span><\/div><\/div><p id=\"fs-id1167829783830\"><strong data-effect=\"bold\">Graph a Line Using Its Slope and Intercept<\/strong><\/p><p>In the following exercises, identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of each line.<\/p><div data-type=\"exercise\" id=\"fs-id1167836524200\"><div data-type=\"problem\" id=\"fs-id1167833369422\"><p>\\(y=-4x+9\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836434016\"><div data-type=\"problem\" id=\"fs-id1167836434018\"><p id=\"fs-id1167836392639\">\\(y=\\frac{5}{3}x-6\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836575631\"><p id=\"fs-id1167836575633\">\\(m=\\frac{5}{3};\\left(0,-6\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836507861\"><div data-type=\"problem\" id=\"fs-id1167833256025\"><p id=\"fs-id1167833256027\">\\(5x+y=10\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829741996\"><div data-type=\"problem\" id=\"fs-id1167829741998\"><p id=\"fs-id1167829619884\">\\(4x-5y=8\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833054991\"><p id=\"fs-id1167836526730\">\\(m=\\frac{4}{5};\\left(0,-\\frac{8}{5}\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167836312931\">In the following exercises, graph the line of each equation using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p><div data-type=\"exercise\" id=\"fs-id1167836558639\"><div data-type=\"problem\" id=\"fs-id1167836408213\"><p id=\"fs-id1167836408215\">\\(y=2x+3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836533072\"><div data-type=\"problem\" id=\"fs-id1167832982331\"><p id=\"fs-id1167832982333\">\\(y=\\text{\u2212}x-1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836375314\"><span data-type=\"media\" id=\"fs-id1167833270225\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_372_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).\"><\/span><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836598001\"><p id=\"fs-id1167836598003\">\\(y=-\\frac{2}{5}x+3\\)<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836535018\"><p id=\"fs-id1167836535020\">\\(4x-3y=12\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833340136\"><span data-type=\"media\" id=\"fs-id1167836493581\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_374_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).\"><\/span><\/div><\/div><p id=\"fs-id1167836558141\">In the following exercises, determine the most convenient method to graph each line.<\/p><div data-type=\"exercise\" id=\"fs-id1167836509786\"><div data-type=\"problem\" id=\"fs-id1167836509788\"><p id=\"fs-id1167824578768\">\\(x=5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829952812\"><div data-type=\"problem\" id=\"fs-id1167825766095\"><p id=\"fs-id1167825766097\">\\(y=-3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836597617\"><p id=\"fs-id1167836597619\">horizontal line<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833060079\"><div data-type=\"problem\" id=\"fs-id1167833060081\"><p>\\(2x+y=5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833059952\"><div data-type=\"problem\" id=\"fs-id1167833059954\"><p id=\"fs-id1167829715877\">\\(x-y=2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836697072\"><p id=\"fs-id1167829787194\">intercepts<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836575255\"><p id=\"fs-id1167836575257\">\\(y=\\frac{2}{2}x+2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836525357\"><div data-type=\"problem\" id=\"fs-id1167836525359\"><p id=\"fs-id1167824766879\">\\(y=\\frac{3}{4}x-1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833138013\"><p id=\"fs-id1167833138015\">plotting points<\/p><\/div><\/div><p id=\"fs-id1167836527756\"><strong data-effect=\"bold\">Graph and Interpret Applications of Slope-Intercept<\/strong><\/p><div data-type=\"exercise\" id=\"fs-id1167826211804\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167826211806\"><p id=\"fs-id1167836717304\">Katherine is a private chef. The equation \\(C=6.5m+42\\) models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of meals, <em data-effect=\"italics\">m<\/em>, that she serves.<\/p><p id=\"fs-id1167836440780\"><span class=\"token\">\u24d0<\/span> Find Katherine\u2019s cost for a week when she serves no meals.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find the cost for a week when she serves 14 meals.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Graph the equation.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829709310\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829709313\"><p id=\"fs-id1167829694607\">Marjorie teaches piano. The equation \\(P=35h-250\\) models the relation between her weekly profit, <em data-effect=\"italics\">P<\/em>, in dollars and the number of student lessons, <em data-effect=\"italics\">s<\/em>, that she teaches.<\/p><p><span class=\"token\">\u24d0<\/span> Find Marjorie\u2019s profit for a week when she teaches no student lessons.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find the profit for a week when she teaches 20 student lessons.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Graph the equation.<\/div><div data-type=\"solution\" id=\"fs-id1167830123744\"><p id=\"fs-id1167830123746\"><span class=\"token\">\u24d0<\/span>\\(\\text{\u2212}\\text{?}250\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> ?450<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> The slope, 35, means that Marjorie\u2019s weekly profit, <em data-effect=\"italics\">P<\/em>, increases by ?35 for each additional student lesson she teaches.<div data-type=\"newline\"><br><\/div> The <em data-effect=\"italics\">P<\/em>-intercept means that when the number of lessons is 0, Marjorie loses ?250.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span><div data-type=\"newline\"><br><\/div> <span data-type=\"media\" id=\"fs-id1167833050702\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_376_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).\"><\/span><\/div><\/div><p id=\"fs-id1167833350392\"><strong data-effect=\"bold\">Use Slopes to Identify Parallel and Perpendicular Lines<\/strong><\/p><p id=\"fs-id1167836705885\">In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.<\/p><div data-type=\"exercise\" id=\"fs-id1167836730415\"><div data-type=\"problem\" id=\"fs-id1167836730417\"><p id=\"fs-id1167833060992\">\\(4x-3y=-1;y=\\frac{4}{3}x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836499090\"><div data-type=\"problem\" id=\"fs-id1167836499092\"><p id=\"fs-id1167833408067\">\\(y=5x-1;10x+2y=0\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829833842\"><p id=\"fs-id1167829833844\">neither<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836717592\"><div data-type=\"problem\" id=\"fs-id1167836717594\"><p id=\"fs-id1167833239045\">\\(3x-2y=5;2x+3y=6\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836792421\"><div data-type=\"problem\"><p id=\"fs-id1167836575517\">\\(2x-y=8;x-2y=4\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836601367\"><p id=\"fs-id1167836601369\">not parallel<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836526512\"><h4 data-type=\"title\"><a href=\"\/contents\/a70487c0-0cc1-4b9b-bed5-8c15bf231b19\" class=\"target-chapter\">Find the Equation of a Line<\/a><\/h4><p id=\"fs-id1167836613250\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong><\/p><p id=\"fs-id1167829861813\">In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167832937076\"><div data-type=\"problem\" id=\"fs-id1167836536612\"><p id=\"fs-id1167836536614\">slope \\(\\frac{1}{3}\\) and \\(y\\)-intercept \\(\\left(0,-6\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833334748\"><div data-type=\"problem\" id=\"fs-id1167829597265\"><p id=\"fs-id1167829597267\">slope \\(-5\\) and \\(y\\)-intercept \\(\\left(0,-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826212238\"><p id=\"fs-id1167826212240\">\\(y=-5x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829597408\"><div data-type=\"problem\" id=\"fs-id1167829597410\"><p id=\"fs-id1167829716068\">slope 0 and \\(y\\)-intercept \\(\\left(0,4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824732674\"><div data-type=\"problem\"><p>slope \\(-2\\) and \\(y\\)-intercept \\(\\left(0,0\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836327049\"><p id=\"fs-id1167836327051\">\\(y=-2x\\)<\/p><\/div><\/div><p id=\"fs-id1167829744040\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167833025723\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829746479\"><span data-type=\"media\" id=\"fs-id1167829746482\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_226_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824733731\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836599996\"><span data-type=\"media\" id=\"fs-id1167836599999\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_227_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836512155\"><p id=\"fs-id1167829751092\">\\(y=-3x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829597335\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829693762\"><span data-type=\"media\" id=\"fs-id1167829693765\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_228_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829921267\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836434329\"><span data-type=\"media\" id=\"fs-id1167836434331\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_229_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836549401\"><p id=\"fs-id1167833086867\">\\(y=-4\\)<\/p><\/div><\/div><p id=\"fs-id1167833346720\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and a Point<\/strong><\/p><p id=\"fs-id1167829718877\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833041788\"><p id=\"fs-id1167833041790\">\\(m=-\\frac{1}{4},\\) point \\(\\left(-8,3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829596447\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829596449\"><p id=\"fs-id1167833175513\">\\(m=\\frac{3}{5},\\) point \\(\\left(10,6\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836645860\"><p id=\"fs-id1167836645862\">\\(y=\\frac{3}{5}x\\)<\/p><\/div><\/div><div data-type=\"exercise\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836684568\"><p id=\"fs-id1167836684570\">Horizontal line containing \\(\\left(-2,7\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829756252\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829756254\"><p id=\"fs-id1167829756256\">\\(m=-2,\\) point \\(\\left(-1,-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836439630\"><p id=\"fs-id1167836439632\">\\(y=-2x-5\\)<\/p><\/div><\/div><p><strong data-effect=\"bold\">Find an Equation of the Line Given Two Points<\/strong><\/p><p id=\"fs-id1167833086732\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167836550894\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836550896\"><p id=\"fs-id1167829789152\">\\(\\left(2,10\\right)\\) and \\(\\left(-2,-2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826169452\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167830093792\"><p id=\"fs-id1167830093794\">\\(\\left(7,1\\right)\\) and \\(\\left(5,0\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836614917\"><p id=\"fs-id1167836613350\">\\(y=\\frac{1}{2}x-\\frac{5}{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829749597\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829749599\"><p id=\"fs-id1167829749601\">\\(\\left(3,8\\right)\\) and \\(\\left(3,-4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824734798\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824734800\"><p id=\"fs-id1167824734802\">\\(\\left(5,2\\right)\\) and \\(\\left(-1,2\\right)\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167833021593\">\\(y=2\\)<\/p><\/div><\/div><p id=\"fs-id1167829596630\"><strong data-effect=\"bold\">Find an Equation of a Line Parallel to a Given Line<\/strong><\/p><p id=\"fs-id1167836366759\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167829784008\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829784010\"><p id=\"fs-id1167829784012\">line \\(y=-3x+6,\\) point \\(\\left(1,-5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836535046\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833339170\"><p id=\"fs-id1167833339172\">line \\(2x+5y=-10,\\) point \\(\\left(10,4\\right)\\)<\/p><\/div><div data-type=\"solution\"><p>\\(y=-\\frac{2}{5}x+8\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836538320\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836538322\"><p id=\"fs-id1167836538324\">line \\(x=4,\\) point \\(\\left(-2,-1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829930155\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829930157\"><p id=\"fs-id1167833345935\">line \\(y=-5,\\) point \\(\\left(-4,3\\right)\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167833340114\">\\(y=3\\)<\/p><\/div><\/div><p id=\"fs-id1167833129252\"><strong data-effect=\"bold\">Find an Equation of a Line Perpendicular to a Given Line<\/strong><\/p><p id=\"fs-id1167824585096\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167824734676\" class=\"material-set-2\"><div data-type=\"problem\"><p id=\"fs-id1167829743859\">line \\(y=-\\frac{4}{5}x+2,\\) point \\(\\left(8,9\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836687826\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836687828\"><p id=\"fs-id1167825003616\">line \\(2x-3y=9,\\) point \\(\\left(-4,0\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829693413\"><p>\\(y=-\\frac{3}{2}x-6\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824739288\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824739290\"><p id=\"fs-id1167825857164\">line \\(y=3,\\) point \\(\\left(-1,-3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836686948\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829627590\"><p id=\"fs-id1167829627592\">line \\(x=-5\\) point \\(\\left(2,1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829721210\"><p id=\"fs-id1167829721212\">\\(y=1\\)<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836570304\"><h4 data-type=\"title\"><a href=\"\/contents\/f15d09b6-aae4-4ad3-a9e6-c9d1ac2436e3\" class=\"target-chapter\">Graph Linear Inequalities in Two Variables<\/a><\/h4><p id=\"fs-id1167832951212\"><strong data-effect=\"bold\">Verify Solutions to an Inequality in Two Variables<\/strong><\/p><p id=\"fs-id1167833272639\">In the following exercises, determine whether each ordered pair is a solution to the given inequality.<\/p><div data-type=\"exercise\" id=\"fs-id1167833052460\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833052463\"><p id=\"fs-id1167833052465\">Determine whether each ordered pair is a solution to the inequality \\(y&lt;x-3\\text{:}\\)<\/p><p><span class=\"token\">\u24d0<\/span>\\(\\left(0,1\\right)\\)<span class=\"token\">\u24d1<\/span>\\(\\left(-2,-4\\right)\\)<span class=\"token\">\u24d2<\/span>\\(\\left(5,2\\right)\\)<span class=\"token\">\u24d3<\/span>\\(\\left(3,-1\\right)\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(\\left(-1,-5\\right)\\)<\/div><\/div><div data-type=\"exercise\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833379475\"><p id=\"fs-id1167836622804\">Determine whether each ordered pair is a solution to the inequality \\(x+y&gt;4\\text{:}\\)<\/p><p id=\"fs-id1167836792019\"><span class=\"token\">\u24d0<\/span>\\(\\left(6,1\\right)\\)<span class=\"token\">\u24d1<\/span>\\(\\left(-3,6\\right)\\)<span class=\"token\">\u24d2<\/span>\\(\\left(3,2\\right)\\)<span class=\"token\">\u24d3<\/span>\\(\\left(-5,10\\right)\\)<span class=\"token\">\u24d4<\/span>\\(\\left(0,0\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836621307\"><p id=\"fs-id1167836621309\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> no <span class=\"token\">\u24d2<\/span> yes <span class=\"token\">\u24d3<\/span> yes; <span class=\"token\">\u24d4<\/span> no<\/p><\/div><\/div><p id=\"fs-id1167833057530\"><strong data-effect=\"bold\">Recognize the Relation Between the Solutions of an Inequality and its Graph<\/strong><\/p><p id=\"fs-id1167836312912\">In the following exercises, write the inequality shown by the shaded region.<\/p><div data-type=\"exercise\" id=\"fs-id1167824841358\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824841360\"><p id=\"fs-id1167824841363\">Write the inequality shown by the graph with the boundary line \\(y=\\text{\u2212}x+2.\\)<\/p><span data-type=\"media\" id=\"fs-id1167833381869\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 2), (1, 1), and (2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_230_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 2), (1, 1), and (2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836515439\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836515442\"><p id=\"fs-id1167836694224\">Write the inequality shown by the graph with the boundary line \\(y=\\frac{2}{3}x-3.\\)<\/p><span data-type=\"media\" id=\"fs-id1167836621666\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (3, negative 1), and (6, 1). The line divides the x y-coordinate plane into two halves. The line and the top left half are shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_231_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (3, negative 1), and (6, 1). The line divides the x y-coordinate plane into two halves. The line and the top left half are shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836432878\"><p id=\"fs-id1167833136729\">\\(y&gt;\\frac{2}{3}x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829688943\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829688945\"><p id=\"fs-id1167836326696\">Write the inequality shown by the shaded region in the graph with the boundary line \\(x+y=-4.\\)<\/p><span data-type=\"media\" id=\"fs-id1167833361642\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (negative 2, negative 2), and (negative 4, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_232_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (negative 2, negative 2), and (negative 4, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832982202\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167832982205\"><p>Write the inequality shown by the shaded region in the graph with the boundary line \\(x-2y=6.\\)<\/p><span data-type=\"media\" id=\"fs-id1167836535109\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (2, negative 2), and (6, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_233_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (2, negative 2), and (6, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836701518\"><p id=\"fs-id1167836701520\">\\(x-2y\\ge 6\\)<\/p><\/div><\/div><p id=\"fs-id1167836509955\"><strong data-effect=\"bold\">Graph Linear Inequalities in Two Variables<\/strong><\/p><p id=\"fs-id1167829921248\">In the following exercises, graph each linear inequality.<\/p><div data-type=\"exercise\" id=\"fs-id1167829921251\"><div data-type=\"problem\" id=\"fs-id1167836392054\"><p id=\"fs-id1167836392056\">Graph the linear inequality \\(y&gt;\\frac{2}{5}x-4.\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833237777\"><div data-type=\"problem\" id=\"fs-id1167833237779\"><p id=\"fs-id1167833237782\">Graph the linear inequality \\(y\\le -\\frac{1}{4}x+3.\\)<\/p><\/div><div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167832937170\" data-alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_378_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836495549\"><p id=\"fs-id1167836495551\">Graph the linear inequality \\(x-y\\le 5.\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836341917\"><div data-type=\"problem\" id=\"fs-id1167836341919\"><p id=\"fs-id1167829783814\">Graph the linear inequality \\(3x+2y&gt;10.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836620995\"><span data-type=\"media\" id=\"fs-id1167836729455\" data-alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_380_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836497114\"><div data-type=\"problem\" id=\"fs-id1167836497116\"><p id=\"fs-id1167836497118\">Graph the linear inequality \\(y\\le -3x.\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833237757\"><div data-type=\"problem\" id=\"fs-id1167829719800\"><p id=\"fs-id1167829719802\">Graph the linear inequality \\(y&lt;6.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829747740\"><span data-type=\"media\" id=\"fs-id1167836530484\" data-alt=\"This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_382_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.\"><\/span><\/div><\/div><p id=\"fs-id1167824734423\"><strong data-effect=\"bold\">Solve Applications using Linear Inequalities in Two Variables<\/strong><\/p><div data-type=\"exercise\" id=\"fs-id1167836567301\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836567303\"><p id=\"fs-id1167836567305\">Shanthie needs to earn at least ?500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays ?10 an hour and the other as an intern in a law office for ?25 hour. How many hours does Shanthie need to work at each job to earn at least ?500 per week?<\/p><p id=\"fs-id1167824734612\"><span class=\"token\">\u24d0<\/span> Let <em data-effect=\"italics\">x<\/em> be the number of hours she works teaching swimming and let <em data-effect=\"italics\">y<\/em> be the number of hours she works as an intern. Write an inequality that would model this situation.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Graph the inequality.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find three ordered pairs \\(\\left(x,y\\right)\\) that would be solutions to the inequality. Then, explain what that means for Shanthie.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836409564\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836409567\"><p id=\"fs-id1167836553948\">Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking.<\/p><p id=\"fs-id1167836553953\"><span class=\"token\">\u24d0<\/span> If <em data-effect=\"italics\">x<\/em> is the number of minutes that Atsushi runs and <em data-effect=\"italics\">y<\/em> is the number minutes he bikes, find the inequality that models the situation.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Graph the inequality.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> List three solutions to the inequality. What options do the solutions provide Atsushi?<\/div><div data-type=\"solution\" id=\"fs-id1167829704678\"><p id=\"fs-id1167829704681\"><span class=\"token\">\u24d0<\/span>\\(20x+15y\\ge 600\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829594005\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_384_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> Answers will vary.<\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167826172554\"><h4 data-type=\"title\"><a href=\"\/contents\/5e548626-8f0f-496d-ab87-4f0358ca2fd3\" class=\"target-chapter\">Relations and Functions<\/a><\/h4><p id=\"fs-id1167836486019\"><strong data-effect=\"bold\">Find the Domain and Range of a Relation<\/strong><\/p><p id=\"fs-id1167833365925\">In the following exercises, for each relation, <span class=\"token\">\u24d0<\/span> find the domain of the relation <span class=\"token\">\u24d1<\/span> find the range of the relation.<\/p><div data-type=\"exercise\" id=\"fs-id1167833056137\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833056139\"><p id=\"fs-id1167836717056\">\\(\\left\\{\\left(5,-2\\right),\\left(5,-4\\right),\\left(7,-6\\right),\\)<\/p><div data-type=\"newline\"><br><\/div>\\(\\left(8,-8\\right),\\left(9,-10\\right)\\right\\}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833053062\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833053064\"><p id=\"fs-id1167836408010\">\\(\\left\\{\\left(-3,7\\right),\\left(-2,3\\right),\\left(-1,9\\right),\\)<\/p><div data-type=\"newline\"><br><\/div>\\(\\left(0,-3\\right),\\left(-1,8\\right)\\right\\}\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829908245\"><p id=\"fs-id1167829908247\"><span class=\"token\">\u24d0<\/span> D: {\u22123, \u22122, \u22121, 0}<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> R: {7, 3, 9, \u22123, 8}<\/div><\/div><p id=\"fs-id1167833346961\">In the following exercise, use the mapping of the relation to <span class=\"token\">\u24d0<\/span> list the ordered pairs of the relation <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836325788\"><div data-type=\"problem\" id=\"fs-id1167836325790\"><p id=\"fs-id1167836325792\">The mapping below shows the average weight of a child according to age.<\/p><span data-type=\"media\" id=\"fs-id1167829685523\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cAge (yrs)\u201d and lists the numbers 1, 2, 3, 4, 5, 6, and 7. The table on the right has the header \u201cWeight (pounds)\u201d and lists the numbers 20, 35, 30, 45, 40, 25, and 50. There are arrows starting at numbers in the age table and pointing towards numbers in the weight table. The first arrow goes from 1 to 20. The second arrow goes from 2 to 25. The third arrow goes from 3 to 30. The fourth arrow goes from 4 to 35. The fifth arrow goes from 5 to 40. The sixth arrow goes from 6 to 45. The seventh arrow goes from 7 to 50.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_234_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cAge (yrs)\u201d and lists the numbers 1, 2, 3, 4, 5, 6, and 7. The table on the right has the header \u201cWeight (pounds)\u201d and lists the numbers 20, 35, 30, 45, 40, 25, and 50. There are arrows starting at numbers in the age table and pointing towards numbers in the weight table. The first arrow goes from 1 to 20. The second arrow goes from 2 to 25. The third arrow goes from 3 to 30. The fourth arrow goes from 4 to 35. The fifth arrow goes from 5 to 40. The sixth arrow goes from 6 to 45. The seventh arrow goes from 7 to 50.\"><\/span><\/div><\/div><p id=\"fs-id1167836597962\">In the following exercise, use the graph of the relation to <span class=\"token\">\u24d0<\/span> list the ordered pairs of the relation <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836368154\"><div data-type=\"problem\" id=\"fs-id1167836368156\"><span data-type=\"media\" id=\"fs-id1167824617025\" data-alt=\"The figure shows the graph of some points on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The points (negative 3, 1), (negative 2, negative 1), (negative 2, negative 3), (0, negative 1), (0, 4), and (4, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_235_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the graph of some points on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The points (negative 3, 1), (negative 2, negative 1), (negative 2, negative 3), (0, negative 1), (0, 4), and (4, 3).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833290236\"><p id=\"fs-id1167833290238\"><span class=\"token\">\u24d0<\/span> (4, 3), (\u22122, \u22123), (\u22122, \u22121), (\u22123, 1), (0, \u22121), (0, 4),<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: {\u22123, \u22122, 0, 4}<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> R: {\u22123, \u22121, 1, 3, 4}<\/div><\/div><p id=\"fs-id1167836691409\"><strong data-effect=\"bold\">Determine if a Relation is a Function<\/strong><\/p><p id=\"fs-id1167836543349\">In the following exercises, use the set of ordered pairs to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p><div data-type=\"exercise\" id=\"fs-id1167836571217\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836487361\"><p id=\"fs-id1167836487363\">\\(\\left\\{\\left(9,-5\\right),\\left(4,-3\\right),\\left(1,-1\\right),\\)<\/p><div data-type=\"newline\"><br><\/div>\\(\\left(0,0\\right),\\left(1,1\\right),\\left(4,3\\right),\\left(9,5\\right)\\right\\}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836319254\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836319256\"><p id=\"fs-id1167833008455\">\\(\\left\\{\\left(-3,27\\right),\\left(-2,8\\right),\\left(-1,1\\right),\\)<\/p><div data-type=\"newline\"><br><\/div>\\(\\left(0,0\\right),\\left(1,1\\right),\\left(2,8\\right),\\left(3,27\\right)\\right\\}\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829695005\"><p id=\"fs-id1167836570181\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> {0, 1, 8, 27}<\/div><\/div><p id=\"fs-id1167836560861\">In the following exercises, use the mapping to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function <span class=\"token\">\u24d1<\/span> find the domain of the function <span class=\"token\">\u24d2<\/span> find the range of the function.<\/p><div data-type=\"exercise\" id=\"fs-id1167833054561\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833054563\"><span data-type=\"media\" id=\"fs-id1167836502048\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fourth power\u201d and lists the numbers 0, 1, 16, and 81. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fourth power table. The first arrow goes from negative 3 to 81. The second arrow goes from negative 2 to 16. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 16. The seventh arrow goes from 3 to 81.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_236_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fourth power\u201d and lists the numbers 0, 1, 16, and 81. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fourth power table. The first arrow goes from negative 3 to 81. The second arrow goes from negative 2 to 16. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 16. The seventh arrow goes from 3 to 81.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824585099\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824585102\"><span data-type=\"media\" id=\"fs-id1167829715306\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fifth power\u201d and lists the numbers 0, 1, 32, 243, negative 1, negative 32, and negative 243. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fifth power table. The first arrow goes from negative 3 to negative 243. The second arrow goes from negative 2 to negative 32. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 32. The seventh arrow goes from 3 to 243.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_237_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fifth power\u201d and lists the numbers 0, 1, 32, 243, negative 1, negative 32, and negative 243. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fifth power table. The first arrow goes from negative 3 to negative 243. The second arrow goes from negative 2 to negative 32. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 32. The seventh arrow goes from 3 to 243.\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167833057444\"><p id=\"fs-id1167824578479\"><span class=\"token\">\u24d0<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> {\u2212243, \u221232, \u22121, 0, 1, 32, 243}<\/div><\/div><p id=\"fs-id1167824736070\">In the following exercises, determine whether each equation is a function.<\/p><div data-type=\"exercise\" id=\"fs-id1167836628928\"><div data-type=\"problem\" id=\"fs-id1167836628930\"><p id=\"fs-id1167836628932\">\\(2x+y=-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833048649\"><div data-type=\"problem\" id=\"fs-id1167824781609\"><p id=\"fs-id1167824781611\">\\(y={x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836409422\"><p id=\"fs-id1167829624646\">yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829930429\"><div data-type=\"problem\" id=\"fs-id1167829930432\"><p id=\"fs-id1167829930434\">\\(y=3x-5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836730447\"><div data-type=\"problem\" id=\"fs-id1167833060680\"><p id=\"fs-id1167833060682\">\\(y={x}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836731997\"><p id=\"fs-id1167836600119\">yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836600124\"><div data-type=\"problem\" id=\"fs-id1167833059199\"><p id=\"fs-id1167833059202\">\\(2x+{y}^{2}=4\\)<\/p><\/div><\/div><p id=\"fs-id1167826092388\"><strong data-effect=\"bold\">Find the Value of a Function<\/strong><\/p><p id=\"fs-id1167833386365\">In the following exercises, evaluate the function:<\/p><p id=\"fs-id1167833386368\"><span class=\"token\">\u24d0<\/span>\\(f\\left(-2\\right)\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(3\\right)\\)<span class=\"token\">\u24d2<\/span>\\(f\\left(a\\right).\\)<\/p><div data-type=\"exercise\" id=\"fs-id1167833396868\"><div data-type=\"problem\" id=\"fs-id1167833396870\"><p id=\"fs-id1167833396872\">\\(f\\left(x\\right)=3x-4\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833309935\"><p id=\"fs-id1167833309937\"><span class=\"token\">\u24d0<\/span>\\(f\\left(-2\\right)=-10\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(3\\right)=5\\)<span class=\"token\">\u24d2<\/span>\\(f\\left(a\\right)=3a-4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836606040\"><div data-type=\"problem\" id=\"fs-id1167833272058\"><p id=\"fs-id1167833272060\">\\(f\\left(x\\right)=-2x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829720100\"><div data-type=\"problem\" id=\"fs-id1167829720102\"><p id=\"fs-id1167824720473\">\\(f\\left(x\\right)={x}^{2}-5x+6\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167829741589\"><span class=\"token\">\u24d0<\/span>\\(f\\left(-2\\right)=20\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(3\\right)=0\\)<span class=\"token\">\u24d2<\/span>\\(f\\left(a\\right)={a}^{2}-5a+6\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836389935\"><div data-type=\"problem\" id=\"fs-id1167824734626\"><p id=\"fs-id1167824734628\">\\(f\\left(x\\right)=3{x}^{2}-2x+1\\)<\/p><\/div><\/div><p id=\"fs-id1167836614042\">In the following exercises, evaluate the function.<\/p><div data-type=\"exercise\" id=\"fs-id1167836614045\"><div data-type=\"problem\" id=\"fs-id1167836614047\"><p id=\"fs-id1167836484624\">\\(g\\left(x\\right)=3{x}^{2}-5x;\\)\\(g\\left(2\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836533819\"><p id=\"fs-id1167836533821\">2<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836560606\"><div data-type=\"problem\" id=\"fs-id1167836560608\"><p id=\"fs-id1167829741858\">\\(F\\left(x\\right)=2{x}^{2}-3x+1;\\)<\/p><div data-type=\"newline\"><br><\/div>\\(F\\left(-1\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826171731\"><div data-type=\"problem\" id=\"fs-id1167826171733\"><p id=\"fs-id1167826171735\">\\(h\\left(t\\right)=4|t-1|+2;\\)\\(h\\left(-3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829751601\"><p id=\"fs-id1167829580281\">18<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829786785\"><div data-type=\"problem\" id=\"fs-id1167829786787\"><p id=\"fs-id1167829786789\">\\(f\\left(x\\right)=\\frac{x+2}{x-1};\\)\\(f\\left(3\\right)\\)<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836699953\"><h4 data-type=\"title\"><a href=\"\/contents\/da9d6ce0-a078-4ca2-97af-8cb374f040f5\" class=\"target-chapter\">Graphs of Functions<\/a><\/h4><p id=\"fs-id1167836597214\"><strong data-effect=\"bold\">Use the Vertical line Test<\/strong><\/p><p id=\"fs-id1167836664665\">In the following exercises, determine whether each graph is the graph of a function.<\/p><div data-type=\"exercise\" id=\"fs-id1167836664668\"><div data-type=\"problem\" id=\"fs-id1167833224393\"><span data-type=\"media\" id=\"fs-id1167833224396\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_238_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836449375\"><p id=\"fs-id1167829579813\">yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832925451\"><div data-type=\"problem\" id=\"fs-id1167832925454\"><span data-type=\"media\" id=\"fs-id1167832925456\" data-alt=\"The figure has an s-shaped function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curve goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_239_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an s-shaped function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curve goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833082044\"><div data-type=\"problem\" id=\"fs-id1167833082046\"><span data-type=\"media\" id=\"fs-id1167833082048\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 5, 0), (5, 0), (0, negative 5), and (0, 5).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_240_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 5, 0), (5, 0), (0, negative 5), and (0, 5).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836391903\"><p id=\"fs-id1167836391905\">no<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836599515\"><div data-type=\"problem\" id=\"fs-id1167836599517\"><span data-type=\"media\" id=\"fs-id1167836620286\" data-alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (2, 2), and (2, negative 2). The left-most point on the graph is (negative 2, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_241_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (2, 2), and (2, negative 2). The left-most point on the graph is (negative 2, 0).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836433992\"><div data-type=\"problem\" id=\"fs-id1167833350356\"><span data-type=\"media\" id=\"fs-id1167833350358\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_242_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167836595548\"><p id=\"fs-id1167833329639\">yes<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833329645\"><div data-type=\"problem\" id=\"fs-id1167833025417\"><span data-type=\"media\" id=\"fs-id1167833025419\" data-alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 3, 0), (negative 4, 2), and (negative 4, negative 2). The curved line on the right goes through the points (3, 0), (4, 2), and (4, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_243_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 3, 0), (negative 4, 2), and (negative 4, negative 2). The curved line on the right goes through the points (3, 0), (4, 2), and (4, negative 2).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836606084\"><div data-type=\"problem\" id=\"fs-id1167836606086\"><span data-type=\"media\" id=\"fs-id1167836606088\" data-alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, negative 1) and goes to the right. The line goes through the points (1, 0), (1, negative 2), (2, 1), and (2, negative 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_244_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, negative 1) and goes to the right. The line goes through the points (1, 0), (1, negative 2), (2, 1), and (2, negative 3).\"><\/span><\/div><div data-type=\"solution\"><p>no<\/p><\/div><\/div><p id=\"fs-id1167836326095\"><strong data-effect=\"bold\">Identify Graphs of Basic Functions<\/strong><\/p><p id=\"fs-id1167826205174\">In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range. Write the domain and range in interval notation.<\/p><div data-type=\"exercise\" id=\"fs-id1167832925596\"><div data-type=\"problem\" id=\"fs-id1167836376381\"><p id=\"fs-id1167836376384\">\\(f\\left(x\\right)=5x+1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836552974\"><div data-type=\"problem\" id=\"fs-id1167836518717\"><p id=\"fs-id1167836518719\">\\(f\\left(x\\right)=-4x-2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836688775\"><p id=\"fs-id1167836688777\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829627499\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_386_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829832341\"><div data-type=\"problem\" id=\"fs-id1167833020320\"><p id=\"fs-id1167833020322\">\\(f\\left(x\\right)=\\frac{2}{3}x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836551845\"><div data-type=\"problem\" id=\"fs-id1167836551847\"><p id=\"fs-id1167836551849\">\\(f\\left(x\\right)=-6\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836706786\"><p id=\"fs-id1167829693240\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836525999\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_388_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836556410\"><div data-type=\"problem\" id=\"fs-id1167836556412\"><p id=\"fs-id1167836556414\">\\(f\\left(x\\right)=2x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836523927\"><div data-type=\"problem\" id=\"fs-id1167836523929\"><p id=\"fs-id1167830093968\">\\(f\\left(x\\right)=3{x}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836429710\"><p id=\"fs-id1167836429712\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829692102\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_390_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,0]<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836598112\"><div data-type=\"problem\" id=\"fs-id1167836598114\"><p id=\"fs-id1167824764197\">\\(f\\left(x\\right)=-\\frac{1}{2}{x}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829580140\"><div data-type=\"problem\" id=\"fs-id1167829580143\"><p id=\"fs-id1167829580145\">\\(f\\left(x\\right)={x}^{2}+2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836387842\"><p id=\"fs-id1167836387844\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836530760\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_392_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826206199\"><div data-type=\"problem\" id=\"fs-id1167826206202\"><p id=\"fs-id1167829899546\">\\(f\\left(x\\right)={x}^{3}-2\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836522697\"><div data-type=\"problem\" id=\"fs-id1167836522699\"><p id=\"fs-id1167836539799\">\\(f\\left(x\\right)=\\sqrt{x+2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833279763\"><p id=\"fs-id1167833279765\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829614418\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_394_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: [\\(-2,\\) \u221e), R: [0,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830093271\"><div data-type=\"problem\" id=\"fs-id1167836599284\"><p id=\"fs-id1167836599286\">\\(f\\left(x\\right)=\\text{\u2212}|x|\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836282824\"><div data-type=\"problem\" id=\"fs-id1167836282826\"><p id=\"fs-id1167836282828\">\\(f\\left(x\\right)=|x|+1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829693686\"><p id=\"fs-id1167829693688\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829696612\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_396_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: [1,\u221e)<\/div><\/div><p id=\"fs-id1167836406656\"><strong data-effect=\"bold\">Read Information from a Graph of a Function<\/strong><\/p><p id=\"fs-id1167836310456\">In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation<\/p><div data-type=\"exercise\" id=\"fs-id1167829580264\"><div data-type=\"problem\" id=\"fs-id1167829580266\"><span data-type=\"media\" id=\"fs-id1167836613537\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_245_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836611953\"><div data-type=\"problem\" id=\"fs-id1167836611955\"><span data-type=\"media\" id=\"fs-id1167822971454\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 2). The line goes through the points (negative 1, 3) and (1, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_246_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 2). The line goes through the points (negative 1, 3) and (1, 3).\"><\/span><\/div><div data-type=\"solution\" id=\"fs-id1167829596916\"><p id=\"fs-id1167829596918\">D: (-\u221e,\u221e), R: [2,\u221e)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829984307\"><div data-type=\"problem\" id=\"fs-id1167836697841\"><span data-type=\"media\" id=\"fs-id1167836697843\" data-alt=\"The figure has a cubic function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 4), (0, 0), and (2, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_247_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cubic function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 4), (0, 0), and (2, 4).\"><\/span><\/div><\/div><p id=\"fs-id1167826077068\">In the following exercises, use the graph of the function to find the indicated values.<\/p><div data-type=\"exercise\" id=\"fs-id1167836445033\"><div data-type=\"problem\"><span data-type=\"media\" id=\"fs-id1167829748062\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_248_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><\/span><p id=\"fs-id1167836622098\"><span class=\"token\">\u24d0<\/span> Find \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find \\(f\\left(\\frac{1}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find \\(f\\left(-\\frac{3}{2}\\pi \\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the \\(x\\)-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the \\(y\\)-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167824720940\"><p id=\"fs-id1167824720942\"><span class=\"token\">\u24d0<\/span>\\(f\\left(x\\right)=0\\)<span class=\"token\">\u24d1<\/span>\\(f\\left(\\pi \\text{\/}2\\right)=1\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(f\\left(-3\\pi \\text{\/}2\\right)=1\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(x\\right)=0\\) for \\(x=-2\\pi ,\\text{\u2212}\\pi ,0,\\pi ,2\\pi \\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> \\(\\left(-2\\pi ,0\\right),\\) \\(\\left(\\text{\u2212}\\pi ,0\\right),\\) \\(\\left(0,0\\right),\\) \\(\\left(\\pi ,0\\right),\\) \\(\\left(2\\pi ,0\\right)\\) \\(\\left(f\\right)\\left(0,0\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d6<\/span> \\(\\left[-2\\pi ,2\\pi \\right]\\) <span class=\"token\">\u24d7<\/span> \\(\\left[-1,1\\right]\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832994434\"><div data-type=\"problem\" id=\"fs-id1167832994436\"><span data-type=\"media\" id=\"fs-id1167836439607\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0). The point (0, 2) is the highest point on the graph.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_249_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0). The point (0, 2) is the highest point on the graph.\"><\/span><p id=\"fs-id1167832926094\"><span class=\"token\">\u24d0<\/span> Find \\(f\\left(0\\right).\\)<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when \\(f\\left(x\\right)=0.\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find the \\(x\\)-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find the \\(y\\)-intercepts.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation.<\/div><\/div><\/div><\/div><div class=\"practice-test\" data-depth=\"1\" id=\"fs-id1167836628671\"><h3 data-type=\"title\">Practice Test<\/h3><div data-type=\"exercise\" id=\"fs-id1167833142400\"><div data-type=\"problem\" id=\"fs-id1167829590736\"><p id=\"fs-id1167829590739\">Plot each point in a rectangular coordinate system.<\/p><p id=\"fs-id1167829590742\"><span class=\"token\">\u24d0<\/span>\\(\\left(2,5\\right)\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(-1,-3\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(0,2\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(-4,\\frac{3}{2}\\right)\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(\\left(5,0\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836499081\"><span data-type=\"media\" id=\"fs-id1167836499084\" data-alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_397_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836556753\"><div data-type=\"problem\" id=\"fs-id1167836556755\"><p id=\"fs-id1167836300560\">Which of the given ordered pairs are solutions to the equation \\(3x-y=6?\\)<\/p><p id=\"fs-id1167836648593\"><span class=\"token\">\u24d0<\/span>\\(\\left(3,3\\right)\\)<span class=\"token\">\u24d1<\/span>\\(\\left(2,0\\right)\\)<span class=\"token\">\u24d2<\/span>\\(\\left(4,-6\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167836476746\">Find the slope of each line shown.<\/p><div data-type=\"exercise\" id=\"fs-id1167836476749\"><div data-type=\"problem\" id=\"fs-id1167833019700\"><p id=\"fs-id1167833019702\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836738269\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 5, 2) (0, negative 1), and (5, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_250_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 5, 2) (0, negative 1), and (5, negative 4).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836688572\" data-alt=\"The figure has a straight vertical line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (2, 0) (2, negative 1), and (2, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_251_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight vertical line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (2, 0) (2, negative 1), and (2, 1).\"><\/span><\/div><div data-type=\"solution\"><p id=\"fs-id1167833412508\"><span class=\"token\">\u24d0<\/span>\\(-\\frac{3}{5}\\)<span class=\"token\">\u24d1<\/span> undefined<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836499109\"><div data-type=\"problem\" id=\"fs-id1167836616459\"><p id=\"fs-id1167836616462\">Find the slope of the line between the points \\(\\left(5,2\\right)\\) and \\(\\left(-1,-4\\right).\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833227002\"><div data-type=\"problem\" id=\"fs-id1167833227005\"><p id=\"fs-id1167829716790\">Graph the line with slope \\(\\frac{1}{2}\\) containing the point \\(\\left(-3,-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829785561\"><span data-type=\"media\" id=\"fs-id1167829893484\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_398_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833048332\"><div data-type=\"problem\" id=\"fs-id1167824725990\"><p id=\"fs-id1167824725992\">Find the intercepts of \\(4x+2y=-8\\) and graph.<\/p><\/div><\/div><p id=\"fs-id1167833345913\"><strong data-effect=\"bold\">Graph the line for each of the following equations.<\/strong><\/p><div data-type=\"exercise\" id=\"fs-id1167836514485\"><div data-type=\"problem\" id=\"fs-id1167836295471\"><p id=\"fs-id1167836295473\">\\(y=\\frac{5}{3}x-1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836700038\"><span data-type=\"media\" id=\"fs-id1167836512979\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_400_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836663988\"><div data-type=\"problem\" id=\"fs-id1167829905989\"><p id=\"fs-id1167829905991\">\\(y=\\text{\u2212}x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836628686\"><div data-type=\"problem\" id=\"fs-id1167836673508\"><p id=\"fs-id1167836673510\">\\(y=2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836393101\"><span data-type=\"media\" id=\"fs-id1167836393105\" data-alt=\"The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_402_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).\"><\/span><\/div><\/div><p id=\"fs-id1167836792029\">Find the equation of each line. Write the equation in slope-intercept form.<\/p><div data-type=\"exercise\" id=\"fs-id1167836792032\"><div data-type=\"problem\" id=\"fs-id1167829790514\"><p id=\"fs-id1167829790516\">slope \\(-\\frac{3}{4}\\) and \\(y\\)-intercept \\(\\left(0,-2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829614537\"><div data-type=\"problem\" id=\"fs-id1167829614539\"><p>\\(m=2,\\) point \\(\\left(-3,-1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829756405\"><p id=\"fs-id1167833138135\">\\(y=2x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836574822\"><div data-type=\"problem\" id=\"fs-id1167836574824\"><p id=\"fs-id1167836574826\">containing \\(\\left(10,1\\right)\\) and \\(\\left(6,-1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824652819\"><div data-type=\"problem\" id=\"fs-id1167824652822\"><p id=\"fs-id1167824652824\">perpendicular to the line \\(y=\\frac{5}{4}x+2,\\) containing the point \\(\\left(-10,3\\right)\\)<\/p><\/div><div data-type=\"solution\"><p>\\(y=-\\frac{4}{5}x-5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836375941\"><div data-type=\"problem\" id=\"fs-id1167836375944\"><p id=\"fs-id1167836375946\">Write the inequality shown by the graph with the boundary line \\(y=\\text{\u2212}x-3.\\)<\/p><span data-type=\"media\" id=\"fs-id1167836447243\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, 0), (0, negative 3), and (1, negative 4). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_252_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, 0), (0, negative 3), and (1, negative 4). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><\/span><\/div><\/div><p id=\"fs-id1167829859341\">Graph each linear inequality.<\/p><div data-type=\"exercise\" id=\"fs-id1167836622063\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829893253\"><p id=\"fs-id1167829893255\">\\(y&gt;\\frac{3}{2}x+5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836477414\"><span data-type=\"media\" id=\"fs-id1167833053641\" data-alt=\"The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_403_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836575646\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836575648\"><p id=\"fs-id1167836575650\">\\(x-y\\ge -4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833369817\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833369819\"><p id=\"fs-id1167824781662\">\\(y\\le -5x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836556454\"><span data-type=\"media\" id=\"fs-id1167829877506\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_405_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><\/span><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833327182\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836418794\"><p id=\"fs-id1167836418796\">Hiro works two part time jobs in order to earn enough money to meet her obligations of at least ?450 a week. Her job at the mall pays ?10 an hour and her administrative assistant job on campus pays ?15 an hour. How many hours does Hiro need to work at each job to earn at least ?450?<\/p><p id=\"fs-id1167832951073\"><span class=\"token\">\u24d0<\/span> Let <em data-effect=\"italics\">x<\/em> be the number of hours she works at the mall and let <em data-effect=\"italics\">y<\/em> be the number of hours she works as administrative assistant. Write an inequality that would model this situation.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d1<\/span> Graph the inequality .<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find three ordered pairs\\(\\left(x,y\\right)\\) that would be solutions to the inequality. Then explain what that means for Hiro.<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833369856\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833369858\"><p id=\"fs-id1167833369860\">Use the set of ordered pairs to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function, <span class=\"token\">\u24d1<\/span> find the domain of the relation, and <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p><p id=\"fs-id1167833310998\">\\(\\left\\{\\left(-3,27\\right),\\left(-2,8\\right),\\left(-1,1\\right),\\left(0,0\\right),\\)<\/p><div data-type=\"newline\"><br><\/div>\\(\\left(1,1\\right),\\left(2,8\\right),\\left(3,27\\right)\\right\\}\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836476899\"><p id=\"fs-id1167836476901\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> \\(\\left\\{-3,-2,-1,0,1,2,3\\right\\}\\) <span class=\"token\">\u24d2<\/span> {0, 1, 8, 27}<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833386954\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833239798\"><p id=\"fs-id1167833239800\">Evaluate the function: <span class=\"token\">\u24d0<\/span> \\(f\\left(-1\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(2\\right)\\) <span class=\"token\">\u24d2<\/span> \\(f\\left(c\\right).\\)<\/p><p id=\"fs-id1167829811921\">\\(f\\left(x\\right)=4{x}^{2}-2x-3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833240317\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829692772\"><p id=\"fs-id1167829692774\">For \\(h\\left(y\\right)=3|y-1|-3,\\) evaluate \\(h\\left(-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832940387\"><p>12<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836554217\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836554219\"><p id=\"fs-id1167836554221\">Determine whether the graph is the graph of a function. Explain your answer.<\/p><span data-type=\"media\" id=\"fs-id1167829715554\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_253_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><\/span><\/div><\/div><p id=\"fs-id1167833223602\">In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range.<\/p><div data-type=\"newline\"><br><\/div>Write the domain and range in interval notation.<div data-type=\"exercise\" id=\"fs-id1167829831137\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829590101\"><p id=\"fs-id1167829590103\">\\(f\\left(x\\right)={x}^{2}+1\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833350601\"><p id=\"fs-id1167836531082\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832971403\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_407_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><\/span><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: [1,\u221e)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833380258\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833380261\"><p id=\"fs-id1167833380263\">\\(f\\left(x\\right)=\\sqrt{x+1}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832940626\"><div data-type=\"problem\" id=\"fs-id1167832940628\"><span data-type=\"media\" id=\"fs-id1167832940630\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, negative 3), (0, negative 4), (1, negative 3), and (2, 0). The lowest point on the graph is (0, negative 4).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_254_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, negative 3), (0, negative 4), (1, negative 3), and (2, 0). The lowest point on the graph is (0, negative 4).\"><\/span><p id=\"fs-id1167836629848\"><span class=\"token\">\u24d1<\/span> Find the \\(y\\)-intercepts.<\/p><div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d2<\/span> Find \\(f\\left(-1\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d3<\/span> Find \\(f\\left(1\\right).\\)<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<div data-type=\"newline\"><br><\/div> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation.<\/div><div data-type=\"solution\" id=\"fs-id1167829831564\"><p id=\"fs-id1167833071738\"><span class=\"token\">\u24d0<\/span>\\(x=-2,2\\)<span class=\"token\">\u24d1<\/span>\\(y=-4\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(f\\left(-1\\right)=-3\\)<span class=\"token\">\u24d3<\/span>\\(f\\left(1\\right)=-3\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> D: (-\u221e,\u221e) <span class=\"token\">\u24d5<\/span> R: [\\(-4,\\) \u221e)<\/div><\/div><\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Use the vertical line test<\/li>\n<li>Identify graphs of basic functions<\/li>\n<li>Read information from a graph of a function<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826157468\" class=\"be-prepared\">\n<p id=\"fs-id1167830095706\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167836665273\" type=\"1\">\n<li>Evaluate: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3a402f8a62a07dd1eb366927c0a3e64f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-412270da883a35542927d07df3d24f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"21\" style=\"vertical-align: 0px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829586631\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Evaluate: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-24ced68c2626e49b1f4ac1b713c02a3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#55;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c51c3f75064093187adce869112ccacb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#45;&#51;&#124;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/05eab039-6d1c-4d80-8c8c-94469164a52c#fs-id1167835365552\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Evaluate: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-65ddaa07508d3929b6969a5e4e6baddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"23\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-41702c6999edcdbb35165cc1e3c6a56c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"36\" style=\"vertical-align: -2px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167833056590\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836579284\">\n<h3 data-type=\"title\">Use the Vertical Line Test<\/h3>\n<p id=\"fs-id1167829579930\">In the last section we learned how to determine if a relation is a function. The relations we looked at were expressed as a set of ordered pairs, a mapping or an equation. We will now look at how to tell if a graph is that of a function.<\/p>\n<p id=\"fs-id1167836691995\">An ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> is a solution of a linear equation, if the equation is a true statement when the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-values of the ordered pair are substituted into the equation.<\/p>\n<p id=\"fs-id1167829924871\">The graph of a linear equation is a straight line where every point on the line is a solution of the equation and every solution of this equation is a point on this line.<\/p>\n<p id=\"fs-id1167836625879\">In <a href=\"#CNX_IntAlg_Figure_03_06_001\" class=\"autogenerated-content\">(Figure)<\/a>, we can see that, in graph of the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fa9ece86fa22640223cce98a0c3eb364_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/> for every <em data-effect=\"italics\">x<\/em>-value there is only one <em data-effect=\"italics\">y<\/em>-value, as shown in the accompanying table.<\/p>\n<div class=\"bc-figure figure\" id=\"CNX_IntAlg_Figure_03_06_001\"><span data-type=\"media\" id=\"fs-id1167836424063\" data-alt=\"plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled y equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label y equals2 x minus 3. The second row is a header row with the headers x, y, and (x, y). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2018\/12\/CNX_IntAlg_Figure_03_06_001_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled y equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label y equals2 x minus 3. The second row is a header row with the headers x, y, and (x, y). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\" \/><\/span><\/div>\n<p>A relation is a function if every element of the domain has exactly one value in the range. So the relation defined by the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> is a function.<\/p>\n<p>If we look at the graph, each vertical dashed line only intersects the line at one point. This makes sense as in a function, for every <em data-effect=\"italics\">x<\/em>-value there is only one <em data-effect=\"italics\">y<\/em>-value.<\/p>\n<p id=\"fs-id1167836600350\">If the vertical line hit the graph twice, the <em data-effect=\"italics\">x<\/em>-value would be mapped to two <em data-effect=\"italics\">y<\/em>-values, and so the graph would not represent a function.<\/p>\n<p id=\"fs-id1167836293137\">This leads us to the vertical line test. A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point. If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/p>\n<div data-type=\"note\" id=\"fs-id1167833386905\">\n<div data-type=\"title\">Vertical Line Test<\/div>\n<p>A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point.<\/p>\n<p id=\"fs-id1167836608075\">If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/p>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836731467\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836579319\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836646294\">Determine whether each graph is the graph of a function.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836552272\" data-alt=\"The figure has two graphs. In graph a there is a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). In graph b there is a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_002_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). In graph b there is a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833102413\">\n<p id=\"fs-id1167836542012\"><span class=\"token\">\u24d0<\/span> Since any vertical line intersects the graph in at most one point, the graph is the graph of a function.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167836557713\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 5, x equalsnegative 3, and x equals3. Each line intersects the slanted line at exactly one point.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_003_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 2), (3, 0), and (6, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 5, x equalsnegative 3, and x equals3. Each line intersects the slanted line at exactly one point.\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> One of the vertical lines shown on the graph, intersects it in two points. This graph does not represent a function.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167833339591\" data-alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 2, x equalsnegative 1, and x equals2. The vertical line x \u2013 negative 2 does not intersect the parabola. The vertical line x equalsnegative 1 intersects the parabola at exactly one point. The vertical line x equals3 intersects the parabola at two separate points.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_004_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The parabola goes through the points (negative 1, 0), (0, 1), (0, negative 1), (3, 2), and (3, negative 2). Three dashed vertical straight lines are drawn at x equalsnegative 2, x equalsnegative 1, and x equals2. The vertical line x \u2013 negative 2 does not intersect the parabola. The vertical line x equalsnegative 1 intersects the parabola at exactly one point. The vertical line x equals3 intersects the parabola at two separate points.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836289482\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167830123185\">\n<div data-type=\"problem\" id=\"fs-id1167836439913\">\n<p id=\"fs-id1167836333903\">Determine whether each graph is the graph of a function.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836728309\" data-alt=\"The figure has two graphs. In graph a there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (0, negative 1), (negative 1, 0), (1, 0), (negative 2, 3), and (2, 3). In graph b there is a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 2, 0), (2, 0), (0, negative 2), and (0, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_005_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (0, negative 1), (negative 1, 0), (1, 0), (negative 2, 3), and (2, 3). In graph b there is a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 2, 0), (2, 0), (0, negative 2), and (0, 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833061214\">\n<p id=\"fs-id1167829879758\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> no<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836537878\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836519221\">\n<div data-type=\"problem\" id=\"fs-id1167836526902\">\n<p id=\"fs-id1167836626524\">Determine whether each graph is the graph of a function.<\/p>\n<p><span data-type=\"media\" data-alt=\"The figure has two graphs. In graph a there is an ellipse graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The ellipse goes through the points (0, negative 3), (negative 2, 0), (2, 0), and (0, 3). In graph b there is a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (2, 0), and (4, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_006_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two graphs. In graph a there is an ellipse graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The ellipse goes through the points (0, negative 3), (negative 2, 0), (2, 0), and (0, 3). In graph b there is a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (2, 0), and (4, 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836700357\">\n<p id=\"fs-id1167829693572\"><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\">Identify Graphs of Basic Functions<\/h3>\n<p id=\"fs-id1167836293187\">We used the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> and its graph as we developed the vertical line test. We said that the relation defined by the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> is a function.<\/p>\n<p id=\"fs-id1167833020798\">We can write this as in function notation as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d14dcd605b7a63fc5f6e5b9160dd7ce0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/> It still means the same thing. The graph of the function is the graph of all ordered pairs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-46f4e740f5384b8d5ea91acb6998fd2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/> So we can write the ordered pairs as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8d08691942d5f50eba60e910257b15ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -4px;\" \/> It looks different but the graph will be the same.<\/p>\n<p id=\"fs-id1167836685520\">Compare the graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> previously shown in <a href=\"#CNX_IntAlg_Figure_03_06_001\" class=\"autogenerated-content\">(Figure)<\/a> with the graph of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5eaf591c6b46c0f97d5b0802f0751675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/> shown in <a href=\"#CNX_IntAlg_Figure_03_06_007\" class=\"autogenerated-content\">(Figure)<\/a>. Nothing has changed but the notation.<\/p>\n<div class=\"bc-figure figure\" id=\"CNX_IntAlg_Figure_03_06_007\"><span data-type=\"media\" id=\"fs-id1167836415144\" data-alt=\"This figure has a graph next to a table. The graph has a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled f of x equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label f of x equals2 x minus 3. The second row is a header row with the headers x, f of x, and (x, f of x). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_007_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. The graph has a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 3), (1, negative 1), and (2, 1). The line is labeled f of x equals2 x minus 3. There are several vertical arrows that relate values on the x-axis to points on the line. The first arrow relates x equalsnegative 2 on the x-axis to the point (negative 2, negative 7) on the line. The second arrow relates x equalsnegative 1 on the x-axis to the point (negative 1, negative 5) on the line. The next arrow relates x equals0 on the x-axis to the point (0, negative 3) on the line. The next arrow relates x equals3 on the x-axis to the point (3, 3) on the line. The last arrow relates x equals4 on the x-axis to the point (4, 5) on the line. The table has 7 rows and 3 columns. The first row is a title row with the label f of x equals2 x minus 3. The second row is a header row with the headers x, f of x, and (x, f of x). The third row has the coordinates negative 2, negative 7, and (negative 2, negative 7). The fourth row has the coordinates negative 1, negative 5, and (negative 1, negative 5). The fifth row has the coordinates 0, negative 3, and (0, negative 3). The sixth row has the coordinates 3, 3, and (3, 3). The seventh row has the coordinates 4, 5, and (4, 5).\" \/><\/span><\/div>\n<div data-type=\"note\" id=\"fs-id1167829598148\">\n<div data-type=\"title\">Graph of a Function<\/div>\n<p id=\"fs-id1167836692382\">The graph of a function is the graph of all its ordered pairs, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> or using function notation, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a682906d58dbb6c8a261b2655f038f8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-46f4e740f5384b8d5ea91acb6998fd2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"equation\" id=\"fs-id1167829719082\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-449a209d6bb57512e5a6183a9e32bbd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#97;&#109;&#101;&#32;&#111;&#102;&#32;&#102;&#117;&#110;&#99;&#116;&#105;&#111;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#38;&#32;&#38;&#32;&#120;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#99;&#111;&#111;&#114;&#100;&#105;&#110;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#100;&#101;&#114;&#101;&#100;&#32;&#112;&#97;&#105;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#38;&#32;&#38;&#32;&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#99;&#111;&#111;&#114;&#100;&#105;&#110;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#100;&#101;&#114;&#101;&#100;&#32;&#112;&#97;&#105;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"335\" style=\"vertical-align: -26px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167836321563\">As we move forward in our study, it is helpful to be familiar with the graphs of several basic functions and be able to identify them.<\/p>\n<p id=\"fs-id1167836665565\">Through our earlier work, we are familiar with the graphs of linear equations. The process we used to decide if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e09b4ae6d312635fcb8ec259a322e66d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/> is a function would apply to all linear equations. All non-vertical linear equations are functions. Vertical lines are not functions as the <em data-effect=\"italics\">x<\/em>-value has infinitely many <em data-effect=\"italics\">y<\/em>-values.<\/p>\n<p id=\"fs-id1167836480334\">We wrote linear equations in several forms, but it will be most helpful for us here to use the slope-intercept form of the linear equation. The slope-intercept form of a linear equation is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-08f367b1234ecf1fe2aac0e288fe4feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#109;&#120;&#43;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/> In function notation, this linear function becomes <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3feee4b107083a3efb8153a1621f041a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#109;&#120;&#43;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">m<\/em> is the slope of the line and <em data-effect=\"italics\">b<\/em> is the <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<p>The domain is the set of all real numbers, and the range is also the set of all real numbers.<\/p>\n<div data-type=\"note\" id=\"fs-id1167833049966\">\n<div data-type=\"title\">Linear Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829790631\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_008_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/div>\n<p id=\"fs-id1167836755080\">We will use the graphing techniques we used earlier, to graph the basic functions.<\/p>\n<div data-type=\"example\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833056074\">\n<div data-type=\"problem\" id=\"fs-id1167836513618\">\n<p id=\"fs-id1167836612024\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8c6b87f65e60a799a9cc3e6b4e1f3add_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#120;&#45;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836546655\">\n<table id=\"fs-id1167836688758\" class=\"unnumbered unstyled\" summary=\"We recognize f of x equalsnegative 2 x minus 4 as a linear function. Find the slope and y-intercept. m equalsnegative 2. b equalsnegative 4. Graph using the slope intercept. The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 4), and (negative 1, negative 2).\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f22c72d363c47b0ef884e30abf043a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">We recognize this as a linear function.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Find the slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ea367e53829041fc22f3341ef4e3ad7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#53;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0edd67c500cfb329fc63c710843d8408_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#53;&#46;&#54;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"54\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Graph using the slope intercept.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829746004\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_009a_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829754438\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836406766\">\n<div data-type=\"problem\" id=\"fs-id1167836601239\">\n<p id=\"fs-id1167833051555\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-62ab3197a172d074b9ccf91ea65a0e8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836660083\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" data-alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (1, negative 4), (0, negative 1), and (negative 1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_301_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (1, negative 4), (0, negative 1), and (negative 1, 2).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833128828\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167824781336\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836406990\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-2191957bf86c1efedee70d480c7c509a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829719238\">\n<p id=\"fs-id1167832925581\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833328995\" data-alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 3), (0, negative 5), and (negative 1, negative 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_302_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a linear function on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The line goes through the points (negative 2, 3), (0, negative 5), and (negative 1, negative 1).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833054733\">The next function whose graph we will look at is called the constant function and its equation is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-553df46a41dd70b0461ecddd50fb4bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#98;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">b<\/em> is any real number. If we replace the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-984a3dd11ed3c9a1f42d61a2defb75e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"36\" style=\"vertical-align: -4px;\" \/> with y, we get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-27334f3a0485b8c07e8c9ebc0be4df6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"45\" style=\"vertical-align: -4px;\" \/> We recognize this as the horizontal line whose <em data-effect=\"italics\">y<\/em>-intercept is <em data-effect=\"italics\">b<\/em>. The graph of the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-553df46a41dd70b0461ecddd50fb4bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#98;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/> is also the horizontal line whose <em data-effect=\"italics\">y<\/em>-intercept is <em data-effect=\"italics\">b<\/em>.<\/p>\n<p id=\"fs-id1167836602424\">Notice that for any real number we put in the function, the function value will be <em data-effect=\"italics\">b<\/em>. This tells us the range has only one value, <em data-effect=\"italics\">b<\/em>.<\/p>\n<div data-type=\"note\" id=\"fs-id1167836494179\">\n<div data-type=\"title\">Constant Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836684877\" data-alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_010_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\" \/><\/span><\/div>\n<div data-type=\"example\" id=\"fs-id1167833142741\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836525068\">\n<div data-type=\"problem\" id=\"fs-id1167824764495\">\n<p id=\"fs-id1167836433572\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-de69bd97a45b526f3cec8116c6d71fc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833060151\">\n<table id=\"fs-id1167836560655\" class=\"unnumbered unstyled\" summary=\"We recognize f of x equals4 as a constant function. The graph will be a horizontal line through (0, 4). The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The line goes through the points (negative 2, 4), (0, 4), and (1, 4).\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-84b4b7bce144a709e7eb9d0ff3c1feae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">We recognize this as a constant function.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">The graph will be a horizontal line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-39c99385521a53a652ee24ad5c5d1086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836514168\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_011a_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836481166\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167824736254\">\n<div data-type=\"problem\" id=\"fs-id1167836557139\">\n<p id=\"fs-id1167824764946\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-38f72d8256362fc71907f79c0a1711dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829878652\">\n<p id=\"fs-id1167836399311\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829851276\" data-alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_303_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, negative 2), (1, negative 2), and (2, negative 2).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836558185\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836487148\">\n<div data-type=\"problem\" id=\"fs-id1167836552606\">\n<p id=\"fs-id1167825091690\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a0b15bafc654f39a6d33123bbfed5934_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836501611\">\n<p id=\"fs-id1167833053412\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836409269\" data-alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3), (1, 3), and (2, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_304_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the graph of a constant function on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 3), (1, 3), and (2, 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836528178\">The identity function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-33f65464b9762caa03f6b0a885508445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"71\" style=\"vertical-align: -4px;\" \/> is a special case of the linear function. If we write it in linear function form, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f18d756a5a42bb421f6e0c5b8a8120ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#120;&#43;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/> we see the slope is 1 and the <em data-effect=\"italics\">y<\/em>-intercept is 0.<\/p>\n<div data-type=\"note\" id=\"fs-id1167824674086\">\n<div data-type=\"title\">Identity Function<\/div>\n<p><span data-type=\"media\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_012_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/div>\n<p id=\"fs-id1167826171267\">The next function we will look at is not a linear function. So the graph will not be a line. The only method we have to graph this function is point plotting. Because this is an unfamiliar function, we make sure to choose several positive and negative values as well as 0 for our x-values.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836683384\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836646170\">\n<div data-type=\"problem\" id=\"fs-id1167833345125\">\n<p id=\"fs-id1167836650008\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bac78978801d31220977b3a0e9009f6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833396805\">\n<p id=\"fs-id1167833339306\">We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart as shown.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167836295348\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 3, 9), (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), (2, 4), and (3, 9). The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx squared, and (x, f of x). The second row has the coordinates negative 3, 9, and (negative 3, 9). The third row has the coordinates negative 2, 4, and (negative 2, 4). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 4, and (2, 4). The seventh row has the coordinates 3, 9, and (3, 9).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_013_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 3, 9), (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), (2, 4), and (3, 9). The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx squared, and (x, f of x). The second row has the coordinates negative 3, 9, and (negative 3, 9). The third row has the coordinates negative 2, 4, and (negative 2, 4). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 4, and (2, 4). The seventh row has the coordinates 3, 9, and (3, 9).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836530814\">\n<div data-type=\"problem\">\n<p>Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bac78978801d31220977b3a0e9009f6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836768461\">\n<p id=\"fs-id1167836731140\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833139707\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_305_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829930524\">\n<div data-type=\"problem\" id=\"fs-id1167829695062\">\n<p id=\"fs-id1167833051245\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1be1d57a2ab45be04aa1b45d2427657e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833237691\">\n<p id=\"fs-id1167836288172\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833197255\" data-alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, negative 4), (negative 1, negative 1), (0, 0), (1, negative 1), and (2, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_306_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph next to a table. In the graph there is a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, negative 4), (negative 1, negative 1), (0, 0), (1, negative 1), and (2, negative 4).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829783193\">Looking at the result in <a href=\"#fs-id1167836683384\" class=\"autogenerated-content\">(Figure)<\/a>, we can summarize the features of the square function. We call this graph a parabola. As we consider the domain, notice any real number can be used as an <em data-effect=\"italics\">x<\/em>-value. The domain is all real numbers.<\/p>\n<p>The range is not all real numbers. Notice the graph consists of values of <em data-effect=\"italics\">y<\/em> never go below zero. This makes sense as the square of any number cannot be negative. So, the range of the square function is all non-negative real numbers.<\/p>\n<div data-type=\"note\" id=\"fs-id1167824617137\">\n<div data-type=\"title\">Square Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829744925\" data-alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_014_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/div>\n<p>The next function we will look at is also not a linear function so the graph will not be a line. Again we will use point plotting, and make sure to choose several positive and negative values as well as 0 for our <em data-effect=\"italics\">x<\/em>-values.<\/p>\n<div data-type=\"example\" id=\"fs-id1167832966170\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836572855\">\n<div data-type=\"problem\" id=\"fs-id1167824701409\">\n<p>Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ca5754295945e92ae635535ff285536b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829756525\">\n<p>We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167833020710\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8). Next to the graph is a table. The table has 6 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx cubed, and (x, f of x). The second row has the coordinates negative 2, negative 8, and (negative 2, negative 8). The third row has the coordinates negative 1, negative 1, and (negative 1, negative 1). The fourth row has the coordinates 0, 0, and (0, 0). The fifth row has the coordinates 1, 1, and (1, 1). The sixth row has the coordinates 2, 8, and (2, 8).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_015_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8). Next to the graph is a table. The table has 6 rows and 3 columns. The first row is a header row with the headers x, f of x equalsx cubed, and (x, f of x). The second row has the coordinates negative 2, negative 8, and (negative 2, negative 8). The third row has the coordinates negative 1, negative 1, and (negative 1, negative 1). The fourth row has the coordinates 0, 0, and (0, 0). The fifth row has the coordinates 1, 1, and (1, 1). The sixth row has the coordinates 2, 8, and (2, 8).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836553231\">\n<div data-type=\"problem\" id=\"fs-id1167833060462\">\n<p id=\"fs-id1167836743450\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ca5754295945e92ae635535ff285536b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836519057\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833056490\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_307_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167832982045\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833196697\">\n<div data-type=\"problem\" id=\"fs-id1167829907663\">\n<p>Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-78faddd4b5c42dae8f94df2a43057cc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836775118\">\n<p id=\"fs-id1167829984244\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836434321\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, 8), (negative 1, 1), (0, 0), (1, negative 1), and (2, negative 8).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_308_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, 8), (negative 1, 1), (0, 0), (1, negative 1), and (2, negative 8).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836598078\">Looking at the result in <a href=\"#fs-id1167832966170\" class=\"autogenerated-content\">(Figure)<\/a>, we can summarize the features of the cube function. As we consider the domain, notice any real number can be used as an <em data-effect=\"italics\">x<\/em>-value. The domain is all real numbers.<\/p>\n<p id=\"fs-id1167836787693\">The range is all real numbers. This makes sense as the cube of any non-zero number can be positive or negative. So, the range of the cube function is all real numbers.<\/p>\n<div data-type=\"note\" id=\"fs-id1167829687218\">\n<div data-type=\"title\">Cube Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836496942\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_016_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/div>\n<p id=\"fs-id1167833023152\">The next function we will look at does not square or cube the input values, but rather takes the square root of those values.<\/p>\n<p id=\"fs-id1167836512756\">Let\u2019s graph the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9e1e51d562f8a01710ff24ec7227dc17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/> and then summarize the features of the function. Remember, we can only take the square root of non-negative real numbers, so our domain will be the non-negative real numbers.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829930477\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833350001\">\n<div data-type=\"problem\" id=\"fs-id1167836569057\">\n<p id=\"fs-id1167833019425\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9e1e51d562f8a01710ff24ec7227dc17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833326611\">\n<p id=\"fs-id1167829921787\">We choose <em data-effect=\"italics\">x<\/em>-values. Since we will be taking the square root, we choose numbers that are perfect squares, to make our work easier. We substitute them in and then create a chart.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167829686050\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph is a table. The table has 5 rows and 3 columns. The first row is a header row with the headers x, f of x equalssquare root of x, and (x, f of x). The second row has the coordinates 0, 0, and (0, 0). The third row has the coordinates 1, 1, and (1, 1). The fourth row has the coordinates 4, 2, and (4, 2). The fifth row has the coordinates 9, 3, and (9, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_017_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph is a table. The table has 5 rows and 3 columns. The first row is a header row with the headers x, f of x equalssquare root of x, and (x, f of x). The second row has the coordinates 0, 0, and (0, 0). The third row has the coordinates 1, 1, and (1, 1). The fourth row has the coordinates 4, 2, and (4, 2). The fifth row has the coordinates 9, 3, and (9, 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836341594\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836378266\">\n<div data-type=\"problem\" id=\"fs-id1167836623811\">\n<p id=\"fs-id1167836730489\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b2d25193160b4d885fd9c76379754ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836525446\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1), (4, 2), and (9, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_309_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1), (4, 2), and (9, 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836650089\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836510334\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836602315\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0bd07944e2845dae7ecba45ed080a716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830077318\">\n<p id=\"fs-id1167833139590\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167824733299\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from negative 10 to 0. The curved half-line starts at the point (0, 0) and then goes down and to the right. The curved half line goes through the points (1, negative 1), (4, negative 2), and (9, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_310_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from negative 10 to 0. The curved half-line starts at the point (0, 0) and then goes down and to the right. The curved half line goes through the points (1, negative 1), (4, negative 2), and (9, negative 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836664843\">\n<div data-type=\"title\">Square Root Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836292233\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_018_img-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/div>\n<p id=\"fs-id1167836299963\">Our last basic function is the absolute value function, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9441bea8b9b3d2878ac07eb853441b00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/> Keep in mind that the absolute value of a number is its distance from zero. Since we never measure distance as a negative number, we will never get a negative number in the range.<\/p>\n<div data-type=\"example\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836417983\">\n<div data-type=\"problem\" id=\"fs-id1167836531216\">\n<p>Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9441bea8b9b3d2878ac07eb853441b00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836707251\">\n<p>We choose <em data-effect=\"italics\">x<\/em>-values. We substitute them in and then create a chart.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167836614974\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). Next to the graph is a table. The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsabsolute value of x, and (x, f of x). The second row has the coordinates negative 3, 3, and (negative 3, 3). The third row has the coordinates negative 2, 2, and (negative 2, 2). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 2, and (2, 2). The eighth row has the coordinates 3, 3, and (3, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_019_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). Next to the graph is a table. The table has 8 rows and 3 columns. The first row is a header row with the headers x, f of x equalsabsolute value of x, and (x, f of x). The second row has the coordinates negative 3, 3, and (negative 3, 3). The third row has the coordinates negative 2, 2, and (negative 2, 2). The fourth row has the coordinates negative 1, 1, and (negative 1, 1). The fifth row has the coordinates 0, 0, and (0, 0). The sixth row has the coordinates 1, 1, and (1, 1). The seventh row has the coordinates 2, 2, and (2, 2). The eighth row has the coordinates 3, 3, and (3, 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833350872\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836441074\">\n<p id=\"fs-id1167836376954\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9441bea8b9b3d2878ac07eb853441b00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833014880\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_311_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836625638\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833378973\">\n<div data-type=\"problem\" id=\"fs-id1167836595957\">\n<p id=\"fs-id1167836349492\">Graph: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-82d1a93847ce79c64bfacab5cf17b646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#124;&#120;&#124;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830123030\">\n<p id=\"fs-id1167836787910\">\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833023118\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The v-shaped line goes through the points (negative 3, negative 3), (negative 2, negative 2), (negative 1, negative 1), (0, 0), (1, negative 1), (2, negative 2), and (3, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_312_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The v-shaped line goes through the points (negative 3, negative 3), (negative 2, negative 2), (negative 1, negative 1), (0, 0), (1, negative 1), (2, negative 2), and (3, negative 3).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836389848\">\n<div data-type=\"title\">Absolute Value Function<\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836335262\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_020_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836386547\">\n<h3 data-type=\"title\">Read Information from a Graph of a Function<\/h3>\n<p id=\"fs-id1167833022366\">In the sciences and business, data is often collected and then graphed. The graph is analyzed, information is obtained from the graph and then often predictions are made from the data.<\/p>\n<p id=\"fs-id1167836620724\">We will start by reading the domain and range of a function from its graph.<\/p>\n<p id=\"fs-id1167836514287\">Remember the domain is the set of all the <em data-effect=\"italics\">x<\/em>-values in the ordered pairs in the function. To find the domain we look at the graph and find all the values of <em data-effect=\"italics\">x<\/em> that have a corresponding value on the graph. Follow the value <em data-effect=\"italics\">x<\/em> up or down vertically. If you hit the graph of the function then <em data-effect=\"italics\">x<\/em> is in the domain.<\/p>\n<p id=\"fs-id1167825884739\">Remember the range is the set of all the <em data-effect=\"italics\">y<\/em>-values in the ordered pairs in the function. To find the range we look at the graph and find all the values of <em data-effect=\"italics\">y<\/em> that have a corresponding value on the graph. Follow the value <em data-effect=\"italics\">y<\/em> left or right horizontally. If you hit the graph of the function then <em data-effect=\"italics\">y<\/em> is in the range.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829756085\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833047462\">\n<div data-type=\"problem\" id=\"fs-id1167829688185\">\n<p id=\"fs-id1167833057048\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836538244\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 3, negative 1), (1.5, 3), and (3, 1). The interval [negative 3, 3] is marked on the horizontal axis. The interval [negative 1, 3] is marked on the vertical axis.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_021_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 3, negative 1), (1.5, 3), and (3, 1). The interval [negative 3, 3] is marked on the horizontal axis. The interval [negative 1, 3] is marked on the vertical axis.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836513079\">\n<p id=\"fs-id1167833158804\">To find the domain we look at the graph and find all the values of <em data-effect=\"italics\">x<\/em> that correspond to a point on the graph. The domain is highlighted in red on the graph. The domain is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bb751f5b51dd57ab8eb558729ff89520_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#51;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"fs-id1167836611195\">To find the range we look at the graph and find all the values of <em data-effect=\"italics\">y<\/em> that correspond to a point on the graph. The range is highlighted in blue on the graph. The range is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b53d9efb8d492b05de4ca7f144d658dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836529485\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167829790459\">\n<p id=\"fs-id1167833316764\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167829597137\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 5, negative 4), (0, negative 3), and (1, 2). The interval [negative 5, 1] is marked on the horizontal axis. The interval [negative 4, 2] is marked on the vertical axis.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_022_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 5, negative 4), (0, negative 3), and (1, 2). The interval [negative 5, 1] is marked on the horizontal axis. The interval [negative 4, 2] is marked on the vertical axis.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836525200\">\n<p id=\"fs-id1167825702858\">The domain is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03b1bce6ad3600446c81dce0d81ea6c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/> The range is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c72bb10f618fc8de58d37425da375eed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829718932\">\n<div data-type=\"problem\" id=\"fs-id1167836515516\">\n<p id=\"fs-id1167836613378\">Use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167833128692\" data-alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 5. The y-axis runs from negative 6 to 4. The curved line segment goes through the points (negative 2, 1), (0, 3), and (4, negative 5). The interval [negative 2, 4] is marked on the horizontal axis. The interval [negative 5, 3] is marked on the vertical axis.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_023_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line segment graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 5. The y-axis runs from negative 6 to 4. The curved line segment goes through the points (negative 2, 1), (0, 3), and (4, negative 5). The interval [negative 2, 4] is marked on the horizontal axis. The interval [negative 5, 3] is marked on the vertical axis.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829807801\">\n<p id=\"fs-id1167836576127\">The domain is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-084443298b9c2ada74bb6bf3f84c2234_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/> The range is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-16ae69eaa6f03e186f6669f042279286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#53;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836515910\">We are now going to read information from the graph that you may see in future math classes.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836731462\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836450768\">\n<p id=\"fs-id1167836323347\">Use the graph of the function to find the indicated values.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836493218\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_024_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 4 to 4. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167836377545\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-40db648ecf072253bb1ff652c7890eb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-601c625af55a165a724ae031d993fc71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"72\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836289629\">\n<p id=\"fs-id1167836507194\"><span class=\"token\">\u24d0<\/span> When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-534b43efb5ec72c9aa9f5eaccec09e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/> the function crosses the <em data-effect=\"italics\">y<\/em>-axis at 0. So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0c7e53cb060a5a91a81691025428e22e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-67b9d185b557b4ab078b680fed2f78ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/> the <em data-effect=\"italics\">y<\/em>-value of the function is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fc343c70c6ffe28a6cd57dfb53f250b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-81b6610ad7b09378bd1ac153f880e0e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"102\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> When <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1b090c4d7b1a3842371536f4c3894255_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"73\" style=\"vertical-align: -6px;\" \/> the <em data-effect=\"italics\">y<\/em>-value of the function is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fc343c70c6ffe28a6cd57dfb53f250b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b7e38b5985e88dc469c615025fa5d41e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"116\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> The function is 0 at the points, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c82f2018bc85577be3e6492824cd93ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"285\" style=\"vertical-align: -4px;\" \/> The <em data-effect=\"italics\">x<\/em>-values when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e84bc16f8e60afab7f006058944b3ae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#44;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;&#32;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> The <em data-effect=\"italics\">x<\/em>-intercepts occur when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03bd81b19337bd478ac4d869320205bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> So the <em data-effect=\"italics\">x<\/em>-intercepts occur when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/> The <em data-effect=\"italics\">x<\/em>-intercepts are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c82f2018bc85577be3e6492824cd93ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"285\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> The <em data-effect=\"italics\">y<\/em>-intercepts occur when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d6889ee3f02f0af137641306363d2da7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> So the <em data-effect=\"italics\">y<\/em>-intercepts occur at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/> The <em data-effect=\"italics\">y<\/em>-intercept is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e9b349d335879ab45d8b79d5850b0860_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> This function has a value when <em data-effect=\"italics\">x<\/em> is from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0acf1c5cd5bad4e9dcc6345e8b578bab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"33\" style=\"vertical-align: 0px;\" \/> to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-299a5b87fe5f3f7a9a4c772ff4fa9bd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#112;&#105;&#32;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"24\" style=\"vertical-align: 0px;\" \/> Therefore, the domain in interval notation is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5d9d2bc6f93ba4945130bb0d874e9884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"76\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> This function values, or <em data-effect=\"italics\">y<\/em>-values go from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> to 1. Therefore, the range, in interval notation, is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e068b06c79619b9686e3243a8ed32b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836507624\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829685616\">\n<div data-type=\"problem\" id=\"fs-id1167836547928\">\n<p id=\"fs-id1167833007616\">Use the graph of the function to find the indicated values.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836539761\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 2), (negative pi, 0), (negative 1 divided by 2 times pi, negative 2), (0, 0), (1 divided by 2 times pi, 2), (pi, 0), (3 divided by 2 times pi, negative 2), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 2) and (1 divided by 2 times pi, 2) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 2) and (3 divided by 2 times pi, negative 2) are the lowest points on the graph. The line extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_025_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 2), (negative pi, 0), (negative 1 divided by 2 times pi, negative 2), (0, 0), (1 divided by 2 times pi, 2), (pi, 0), (3 divided by 2 times pi, negative 2), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 2) and (1 divided by 2 times pi, 2) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 2) and (3 divided by 2 times pi, negative 2) are the lowest points on the graph. The line extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167836418791\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03db5c50c4889b2ea21ecbce94fe4746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c08f879de62dd3bade0e4e3b208e2159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"72\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829753187\">\n<p id=\"fs-id1167836550513\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b12261fc628a033b58817f7b0f196b8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c77fb227344e7df2386c38a40cfcff08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"94\" style=\"vertical-align: -7px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ab63f1884b7c231d7b98b2750f7846a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"112\" style=\"vertical-align: -7px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e17d900b95ffe355261eb2f5f031a00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#44;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"149\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4b8a091d5639c00d75d5d2a6fe85cf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"278\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d5<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d6<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9eca553659abf52ff7aa918edb1566c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -5px;\" \/> <span class=\"token\">\u24d7<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-11b3220e14bee50aca89fabdf70fc693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829999559\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836510817\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167833240128\">Use the graph of the function to find the indicated values.<\/p>\n<p><span data-type=\"media\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 1), (negative 3 divided by 2 times pi, 0), (negative pi, negative 1), (negative 1 divided by 2 times pi, 0), (0, 1), (1 divided by 2 times pi, 0), (pi, negative 1), (3 divided by 2 times pi, 0), and (2 times pi, 1). The points (negative 2 times pi, 1), (0, 1), and (2 times pi, 1) are the highest points on the graph. The points (negative pi, negative 1) and (pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_026_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 1), (negative 3 divided by 2 times pi, 0), (negative pi, negative 1), (negative 1 divided by 2 times pi, 0), (0, 1), (1 divided by 2 times pi, 0), (pi, negative 1), (3 divided by 2 times pi, 0), and (2 times pi, 1). The points (negative 2 times pi, 1), (0, 1), and (2 times pi, 1) are the highest points on the graph. The points (negative pi, negative 1) and (pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167836526481\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f1793fa62e93e67e1348f2269f2c5ab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-626e6f5012fffc5a3be9b55f82a80a07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836378109\">\n<p id=\"fs-id1167836612647\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-16799a34d6eff0b6bd5102fdd887f230_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-04f7586c66ac962350f021dfc867880c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0f1aabfae624e6912dd0dcba3a55810c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-2318dfe0041c543685ad4c152c765221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;&#44;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#92;&#112;&#105;&#32;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -6px;\" \/> <span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-688a7172c6515c6d7c77c8f084752776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"294\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d5<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d6<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-992f7d4358b5318b11f44f8c932db1cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -5px;\" \/> <span class=\"token\">\u24d7<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1948771fa2147c98ce700fec79ed4bf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"media-2\">\n<p id=\"fs-id1167836362135\">Access this online resource for additional instruction and practice with graphs of functions.<\/p>\n<ul id=\"fs-id1167836509634\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/37domainrange\">Find Domain and Range<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836597228\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167833036726\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Vertical Line Test<\/strong>\n<ul id=\"fs-id1167836612581\" data-bullet-style=\"bullet\">\n<li>A set of points in a rectangular coordinate system is the graph of a function if every vertical line intersects the graph in at most one point.<\/li>\n<li>If any vertical line intersects the graph in more than one point, the graph does not represent a function.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Graph of a Function<\/strong>\n<ul id=\"fs-id1167836386300\" data-bullet-style=\"bullet\">\n<li>The graph of a function is the graph of all its ordered pairs, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> or using function notation, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a682906d58dbb6c8a261b2655f038f8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-46f4e740f5384b8d5ea91acb6998fd2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"equation\" id=\"fs-id1167836706023\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-449a209d6bb57512e5a6183a9e32bbd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#97;&#109;&#101;&#32;&#111;&#102;&#32;&#102;&#117;&#110;&#99;&#116;&#105;&#111;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#38;&#32;&#38;&#32;&#120;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#99;&#111;&#111;&#114;&#100;&#105;&#110;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#100;&#101;&#114;&#101;&#100;&#32;&#112;&#97;&#105;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#38;&#32;&#38;&#32;&#121;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#99;&#111;&#111;&#114;&#100;&#105;&#110;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#100;&#101;&#114;&#101;&#100;&#32;&#112;&#97;&#105;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"335\" style=\"vertical-align: -26px;\" \/><\/div>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Linear Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833240439\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_027_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsm x plus b\u201d, \u201cm, b: all real numbers\u201d, \u201cm: slope of the line\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Constant Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836699152\" data-alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_028_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight horizontal line on the x y-coordinate plane. The line goes through the point (0, b). Next to the graph are the following: \u201cf of x equalsb\u201d, \u201cb: any real number\u201d, \u201cb: y-intercept\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: b\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Identity Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167826129331\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_029_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The line goes through the points (0, 0), (1, 1), and (2, 2). Next to the graph are the following: \u201cf of x equalsx\u201d, \u201cm: 1\u201d, \u201cb: 0\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Square Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836612513\" data-alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_030_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The parabola goes through the points (negative 2, 4), (negative 1, 1), (0, 0), (1, 1), and (2, 4). Next to the graph are the following: \u201cf of x equalsx squared\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Cube Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833380845\" data-alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_031_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The curved line goes through the points (negative 2, negative 8), (negative 1, negative 1), (0, 0), (1, 1), and (2, 8).). Next to the graph are the following: \u201cf of x equalsx cubed\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: (negative infinity, infinity)\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Square Root Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833245744\" data-alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_032_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a curved half-line graphed on the x y-coordinate plane. The x-axis runs from 0 to 8. The y-axis runs from 0 to 8. The curved half-line starts at the point (0, 0) and then goes up and to the right. The curved half line goes through the points (1, 1) and (4, 2). Next to the graph are the following: \u201cf of x equalssquare root of x\u201d, \u201cDomain: [0, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/li>\n<li><strong data-effect=\"bold\">Absolute Value Function<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836602267\" data-alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_033_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a v-shaped line graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 4. The y-axis runs from negative 1 to 6. The v-shaped line goes through the points (negative 3, 3), (negative 2, 2), (negative 1, 1), (0, 0), (1, 1), (2, 2), and (3, 3). The point (0, 0) where the line changes slope is called the vertex. Next to the graph are the following: \u201cf of x equalsabsolute value of x\u201d, \u201cDomain: (negative infinity, infinity)\u201d, and \u201cRange: [0, infinity)\u201d.\" \/><\/span><\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836310305\">\n<h3 data-type=\"title\">Section Exercises<\/h3>\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167836300671\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167829833896\"><strong data-effect=\"bold\">Use the Vertical Line Test<\/strong><\/p>\n<p>In the following exercises, determine whether each graph is the graph of a function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833256037\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829644953\">\n<p id=\"fs-id1167836620309\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832998983\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 3, 0), (3, 0), (0, negative 3), and (0, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_201_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 3, 0), (3, 0), (0, negative 3), and (0, 3).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836315012\" data-alt=\"The figure has a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (1, 3), (0, 2), (1, 3), and (2, 6).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_202_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening up graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (1, 3), (0, 2), (1, 3), and (2, 6).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836410565\">\n<p id=\"fs-id1167836361332\"><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833059978\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829579698\">\n<p id=\"fs-id1167829720945\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836341027\" data-alt=\"The figure has an s-shaped curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The s-shaped curved line goes through the points (negative 1, 1), (0, 0), and (1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_203_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an s-shaped curved line graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The s-shaped curved line goes through the points (negative 1, 1), (0, 0), and (1, 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829713245\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 4, 0), (4, 0), (0, negative 4), and (0, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_204_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 4, 0), (4, 0), (0, negative 4), and (0, 4).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836628720\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836529276\">\n<p id=\"fs-id1167836621660\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836662706\" data-alt=\"The figure has a parabola opening right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (negative 2, 2), and (2, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_205_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (negative 2, 2), and (2, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833379683\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_206_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836665260\">\n<p><span class=\"token\">\u24d0<\/span> no <span class=\"token\">\u24d1<\/span> yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836362052\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836612768\">\n<p id=\"fs-id1167829589830\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836322912\" data-alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 2, 0), (negative 4, 5), and (negative 4, negative 5). The curved line on the right goes through the points (2, 0), (4, 5), and (4, negative 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_207_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 2, 0), (negative 4, 5), and (negative 4, negative 5). The curved line on the right goes through the points (2, 0), (4, 5), and (4, negative 5).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" data-alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, 2) and goes to the right. The line goes through the points (1, 3), (2, 4), (1, 1), and (2, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_208_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, 2) and goes to the right. The line goes through the points (1, 3), (2, 4), (1, 1), and (2, 0).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167833377170\"><strong data-effect=\"bold\">Identify Graphs of Basic Functions<\/strong><\/p>\n<p>In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range. Write the domain and range in interval notation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836665073\">\n<div data-type=\"problem\" id=\"fs-id1167836477133\">\n<p id=\"fs-id1167836330144\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4496bc44aea2b734c9eca2a432647155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836296139\">\n<p id=\"fs-id1167829849369\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836356672\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, negative 2), (negative 1, 1), and (0, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_313_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, negative 2), (negative 1, 1), and (0, 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829936987\">\n<div data-type=\"problem\" id=\"fs-id1167832945825\">\n<p id=\"fs-id1167833058860\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f6832b3455156a6dcbe83eb72fcd971a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824736142\">\n<div data-type=\"problem\" id=\"fs-id1167824649348\">\n<p id=\"fs-id1167836560312\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b195ddb30e6b6ba7e38444610b673ceb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833350800\">\n<p id=\"fs-id1167836299759\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836530065\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 2), and (2, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_315_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, negative 2), and (2, negative 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829624127\">\n<div data-type=\"problem\" id=\"fs-id1167833082143\">\n<p id=\"fs-id1167836362620\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7ebd37f1bf3a6b4b47b98cddfd45fbe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836694784\">\n<div data-type=\"problem\" id=\"fs-id1167836312665\">\n<p id=\"fs-id1167836615461\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1a27e8e76c1e6ee6b648d003d45bb8d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826025216\">\n<p id=\"fs-id1167833269954\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836717417\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 2), (negative 1, 0), and (0, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_317_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 2), (negative 1, 0), and (0, negative 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836418803\">\n<div data-type=\"problem\" id=\"fs-id1167833128282\">\n<p id=\"fs-id1167829931393\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ab74b88a4568503374ea5c70f490c58a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833128830\">\n<div data-type=\"problem\" id=\"fs-id1167829880227\">\n<p id=\"fs-id1167836732495\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bc4e132dc2c3ef436a5693b5d278d7d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"112\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836516066\">\n<p id=\"fs-id1167836628122\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832936324\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, 1), and (2, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_319_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 0), (0, 1), and (2, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824658727\">\n<div data-type=\"problem\" id=\"fs-id1167836361338\">\n<p id=\"fs-id1167833256412\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-771751de3bfb470cfd4ea543b12fd2d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"112\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836544127\">\n<div data-type=\"problem\" id=\"fs-id1167836319404\">\n<p id=\"fs-id1167824732917\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-89e7d21e9b6530d6e6731a14e8a0a291_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836407696\">\n<p id=\"fs-id1167836649918\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829878394\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 5), and (0, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_321_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 5), and (0, 5).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:{5}<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836429353\">\n<div data-type=\"problem\" id=\"fs-id1167836310954\">\n<p id=\"fs-id1167836282751\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4a863a7bff6459540d0d241a71243de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829745945\">\n<div data-type=\"problem\" id=\"fs-id1167836520136\">\n<p id=\"fs-id1167836546248\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-88b398517a8fd92e3e380be44e696ed2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836510430\">\n<p id=\"fs-id1167836706859\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836513491\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, negative 3), (1, negative 3), and (2, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_323_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, negative 3), (1, negative 3), and (2, negative 3).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-671de90e727e217bcb1d3b9cc3969120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829719517\">\n<div data-type=\"problem\" id=\"fs-id1167829807022\">\n<p id=\"fs-id1167836635569\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-eb64a4432caf09326d154d8d3476e302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836731888\">\n<div data-type=\"problem\" id=\"fs-id1167836685446\">\n<p id=\"fs-id1167836712402\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d268a37dadc23b636bc6955a3e233880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836545379\">\n<p id=\"fs-id1167836550226\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836447279\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 0), (2, 4), and (negative 2, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_325_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 0), (2, 4), and (negative 2, negative 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836626104\">\n<div data-type=\"problem\" id=\"fs-id1167836662613\">\n<p id=\"fs-id1167836552854\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-435af59836f3286bcd17e175f2839b53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836621812\">\n<div data-type=\"problem\" id=\"fs-id1167833310489\">\n<p id=\"fs-id1167833135075\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-de2580a5fb192f19c67c1e1cbe81c8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836330168\">\n<p id=\"fs-id1167836539196\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836691433\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 0), (1, negative 2), and (negative 1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_327_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 12 to 12. The y-axis runs from negative 12 to 12. The line goes through the points (0, 0), (1, negative 2), and (negative 1, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829599925\">\n<div data-type=\"problem\" id=\"fs-id1167829851557\">\n<p id=\"fs-id1167826177592\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-97b45c58c465b9aa47b86b1b6486fd4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"94\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836698477\">\n<div data-type=\"problem\" id=\"fs-id1167836625081\">\n<p id=\"fs-id1167836533854\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db389f37d0e530d042a159db23e61866_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836296574\">\n<p id=\"fs-id1167829830462\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829719707\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_329_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:[0,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836481202\">\n<div data-type=\"problem\" id=\"fs-id1167836613666\">\n<p id=\"fs-id1167833021907\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-71b9184acf1857940c069ac7852062d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836722566\">\n<div data-type=\"problem\" id=\"fs-id1167836730654\">\n<p id=\"fs-id1167836361907\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-169f4d1264d95b77d650078d6157317e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832976376\">\n<p id=\"fs-id1167836522879\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833186678\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 10 to 2. The parabola goes through the points (negative 1, negative 3), (0, 0), and (1, negative 3). The highest point on the graph is (0, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_331_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 10 to 2. The parabola goes through the points (negative 1, negative 3), (0, 0), and (1, negative 3). The highest point on the graph is (0, 0).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:(-\u221e,0]<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836549919\">\n<div data-type=\"problem\" id=\"fs-id1167836326911\">\n<p id=\"fs-id1167836492164\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fc824c3ab32a9545fc1e6b93adba8909_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836321873\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836319029\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-395f327411241134f1dd2a8ec1f36227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824765152\">\n<p id=\"fs-id1167836510523\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829749853\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 4, 8), (negative 2, 2), (0, 0), (2, 2), and (4, 8). The lowest point on the graph is (0, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_333_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 4, 8), (negative 2, 2), (0, 0), (2, 2), and (4, 8). The lowest point on the graph is (0, 0).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:[-\u221e,0)<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167824732033\">\n<p id=\"fs-id1167836329509\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-86da4af9086fd15b7c78edd450d5543b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167826169717\">\n<p id=\"fs-id1167829878789\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7a294c15a253d64d5494761235c0cd07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836362657\">\n<p id=\"fs-id1167836556201\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833025407\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 3), (negative 1, 0), (0, negative 1), (1, 0), and (2, 3). The lowest point on the graph is (0, negative 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_335_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 3), (negative 1, 0), (0, negative 1), (1, 0), and (2, 3). The lowest point on the graph is (0, negative 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> (-\u221e,\u221e), R:[<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df802eaa8e08eb73e8cd4d30d23d4b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/> \u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836662424\">\n<div data-type=\"problem\" id=\"fs-id1167833082497\">\n<p id=\"fs-id1167829689678\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-06b3023d1afd2381670ac606e243fa66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829650694\">\n<div data-type=\"problem\" id=\"fs-id1167836791239\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-313c0c74419df60e91a60dcd2b00a4d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829695009\">\n<p id=\"fs-id1167833346213\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833051204\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_337_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 2), (0, 0), and (1, negative 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836693431\">\n<div data-type=\"problem\" id=\"fs-id1167836602619\">\n<p id=\"fs-id1167836526432\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e307eb250dd2f2ee20d3b62982dcc411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836341365\">\n<div data-type=\"problem\" id=\"fs-id1167833056424\">\n<p id=\"fs-id1167829750112\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e8ce9ff0d000e5cdcea1bbab609afb95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836717043\">\n<p id=\"fs-id1167824584281\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829688798\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_339_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:(-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836415699\">\n<div data-type=\"problem\" id=\"fs-id1167836699822\">\n<p id=\"fs-id1167836701108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-866d5be9775b49e9233d3bb51965e5af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836481043\">\n<div data-type=\"problem\" id=\"fs-id1167826132631\">\n<p id=\"fs-id1167836375975\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-523c61f29e1a27f2a4e9c1355f9e26c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833142040\">\n<p id=\"fs-id1167836310146\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836510096\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (0, 0) and goes through the points (1, 2) and (4, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_341_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (0, 0) and goes through the points (1, 2) and (4, 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:[0,\u221e), R:[0,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833054162\">\n<div data-type=\"problem\" id=\"fs-id1167836521944\">\n<p id=\"fs-id1167836322682\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c15378d5349cbd9709dce011d5bc3d93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836510676\">\n<div data-type=\"problem\" id=\"fs-id1167836624651\">\n<p id=\"fs-id1167836455857\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-31dba1e5d91fa44f13506443c9001dc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#45;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826170204\">\n<p id=\"fs-id1167836514110\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836511382\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_343_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:[1,\u221e), R:[0,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829589762\">\n<div data-type=\"problem\" id=\"fs-id1167836368147\">\n<p id=\"fs-id1167836628623\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-43c17acca432bef6d69ec5e666e5ac4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829923887\">\n<div data-type=\"problem\" id=\"fs-id1167824766922\">\n<p id=\"fs-id1167836409493\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b609f0acc49a35c840695960e54ada6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#124;&#120;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833186644\">\n<p><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836774098\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 0). The line goes through the points (negative 1, 3) and (1, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_345_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 0). The line goes through the points (negative 1, 3) and (1, 3).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:[ <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df802eaa8e08eb73e8cd4d30d23d4b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/> \u221e), R:[\u2212\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829789446\">\n<div data-type=\"problem\" id=\"fs-id1167833397067\">\n<p id=\"fs-id1167836556358\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f2c56075d984982d270071df282b221a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#124;&#120;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"102\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836393413\">\n<div data-type=\"problem\" id=\"fs-id1167829899539\">\n<p id=\"fs-id1167829936852\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c283188375e83dc1c1c38853b16cc3bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836608457\">\n<p id=\"fs-id1167836550967\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833024700\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_347_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D:(-\u221e,\u221e), R:[1,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836601960\">\n<div data-type=\"problem\" id=\"fs-id1167836608052\">\n<p id=\"fs-id1167829712186\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-40dfc650e3b4e37d8d30b0f3840d3144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836686005\"><strong data-effect=\"bold\">Read Information from a Graph of a Function<\/strong><\/p>\n<p id=\"fs-id1167836579171\">In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836580012\">\n<div data-type=\"problem\" id=\"fs-id1167836524810\"><span data-type=\"media\" id=\"fs-id1167832999715\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 8. The half-line starts at the point (2, 0) and goes through the points (3, 1) and (6, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_209_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 8. The half-line starts at the point (2, 0) and goes through the points (3, 1) and (6, 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836524162\">\n<p>D: [2,\u221e), R: [0,\u221e)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836442468\">\n<div data-type=\"problem\" id=\"fs-id1167829624940\"><span data-type=\"media\" id=\"fs-id1167836285461\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_210_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 2 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 3, 0) and goes through the points (negative 2, 1) and (1, 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836692203\">\n<div data-type=\"problem\" id=\"fs-id1167836504168\"><span data-type=\"media\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from 0 to 12. The vertex is at the point (0, 4). The line goes through the points (negative 2, 6) and (2, 6).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_211_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from 0 to 12. The vertex is at the point (0, 4). The line goes through the points (negative 2, 6) and (2, 6).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836293141\">\n<p id=\"fs-id1167824590509\">D: (-\u221e,\u221e), R: [4,\u221e)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836361313\">\n<div data-type=\"problem\" id=\"fs-id1167836363597\"><span data-type=\"media\" id=\"fs-id1167829717427\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The vertex is at the point (0, negative 1). The line goes through the points (negative 1, 0) and (1, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_212_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The vertex is at the point (0, negative 1). The line goes through the points (negative 1, 0) and (1, 0).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836609509\">\n<div data-type=\"problem\" id=\"fs-id1167836557691\"><span data-type=\"media\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_213_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836688268\">\n<p id=\"fs-id1167836574099\">D: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8fd9a5f1c66188e07064702c202786cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -5px;\" \/> R: [0, 2]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833007602\">\n<div data-type=\"problem\" id=\"fs-id1167829684137\"><span data-type=\"media\" id=\"fs-id1167836545772\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The curved line segment starts at the point (negative 3, 3). The line goes through the point (0, 6) and ends at the point (3, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_214_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The curved line segment starts at the point (negative 3, 3). The line goes through the point (0, 6) and ends at the point (3, 3).\" \/><\/span><\/div>\n<\/div>\n<p>In the following exercises, use the graph of the function to find the indicated values.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829831353\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829590096\"><span data-type=\"media\" id=\"fs-id1167836570194\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, negative 1), (negative pi, 0), (negative 1 divided by 2 times pi, 1), (0, 0), (1 divided by 2 times pi, negative 1), (pi, 0), (3 divided by 2 times pi, 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, negative 1) and (1 divided by 2 times pi, negative 1) are the lowest points on the graph. The points (negative 1 divided by 2 times pi, 1) and (3 divided by 2 times pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_215_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, negative 1), (negative pi, 0), (negative 1 divided by 2 times pi, 1), (0, 0), (1 divided by 2 times pi, negative 1), (pi, 0), (3 divided by 2 times pi, 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, negative 1) and (1 divided by 2 times pi, negative 1) are the lowest points on the graph. The points (negative 1 divided by 2 times pi, 1) and (3 divided by 2 times pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167836645558\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03db5c50c4889b2ea21ecbce94fe4746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c08f879de62dd3bade0e4e3b208e2159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"72\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829712368\">\n<p id=\"fs-id1167836441031\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b12261fc628a033b58817f7b0f196b8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-46c91b46eaeff953092e440bd7eb9316_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#47;&#125;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-abf4ebeb0636ce42c29c0c95ba643165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#47;&#125;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a9b31d63d5f23dd1cb85d472823fdfd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"165\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a09f34cc052117664956e1e34c012273_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-22c921be65cdab505b2d9e8a50c99613_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"159\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-95b91def952d7c613d9b21978673ec31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d6<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-992f7d4358b5318b11f44f8c932db1cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#44;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#105;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -5px;\" \/> <span class=\"token\">\u24d7<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1948771fa2147c98ce700fec79ed4bf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832950981\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829849533\"><span data-type=\"media\" id=\"fs-id1167836626610\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, negative 1), (negative 3 divided by 2 times pi, 0), (negative pi, 1), (negative 1 divided by 2 times pi, 0), (0, negative 1), (1 divided by 2 times pi, 0), (pi, 1), (3 divided by 2 times pi, 0), and (2 times pi, negative 1). The points (negative 2 times pi, negative 1) and (2 times pi, negative 1) are the lowest points on the graph. The points (negative pi, 1) and (pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_216_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, negative 1), (negative 3 divided by 2 times pi, 0), (negative pi, 1), (negative 1 divided by 2 times pi, 0), (0, negative 1), (1 divided by 2 times pi, 0), (pi, 1), (3 divided by 2 times pi, 0), and (2 times pi, negative 1). The points (negative 2 times pi, negative 1) and (2 times pi, negative 1) are the lowest points on the graph. The points (negative pi, 1) and (pi, 1) are the highest points on the graph. The pattern extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167829696672\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f1793fa62e93e67e1348f2269f2c5ab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-626e6f5012fffc5a3be9b55f82a80a07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836573407\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836432065\"><span data-type=\"media\" data-alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 3, 2). The line goes through the point (0, 5) and ends at the point (3, 2). The point (0, 5) is the highest point on the graph. The points (negative 3, 2) and (3, 2) are the lowest points on the graph.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_217_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 3, 2). The line goes through the point (0, 5) and ends at the point (3, 2). The point (0, 5) is the highest point on the graph. The points (negative 3, 2) and (3, 2) are the lowest points on the graph.\" \/><\/span><\/p>\n<p id=\"fs-id1167836609689\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-11c792047cb390d4fdc949888c1ce404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e2d15f1465e8ad2b3d524cbce299db86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836544041\">\n<p id=\"fs-id1167829714553\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0d53afe50dcb163f2b507f748db4c40c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fdc3c4c9e413fcb8bcc6942a5e1ec7fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d1c8d056ca3668e36668aba9762b7bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> for no <em data-effect=\"italics\">x<\/em> <span class=\"token\">\u24d4<\/span> none <span class=\"token\">\u24d5<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-17932c1f62fa0296571e88ce8fc0a117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d6<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d6177c786bcac10fac43f1de9f57af7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#51;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d7<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-570184b574e55d357e60c1ce72bafbfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#51;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829859771\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833057178\"><span data-type=\"media\" id=\"fs-id1167836525312\" data-alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 4, 0). The line goes through the point (0, 4) and ends at the point (4, 0). The point (0, 4) is the highest point on the graph. The points (negative 4, 0) and (4, 0) are the lowest points on the graph.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_218_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has the top half of a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The curved line segment starts at the point (negative 4, 0). The line goes through the point (0, 4) and ends at the point (4, 0). The point (0, 4) is the highest point on the graph. The points (negative 4, 0) and (4, 0) are the lowest points on the graph.\" \/><\/span><\/p>\n<p id=\"fs-id1167836409782\"><span class=\"token\">\u24d0<\/span> Find: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find the <em data-effect=\"italics\">x<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836602786\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167836629192\">\n<div data-type=\"problem\" id=\"fs-id1167829599508\">\n<p id=\"fs-id1167833060329\">Explain in your own words how to find the domain from a graph.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830004585\">\n<div data-type=\"problem\" id=\"fs-id1167836613527\">\n<p id=\"fs-id1167832977072\">Explain in your own words how to find the range from a graph.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836790091\">\n<div data-type=\"problem\" id=\"fs-id1167836514007\">\n<p id=\"fs-id1167833057205\">Explain in your own words how to use the vertical line test.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833381224\">\n<div data-type=\"problem\" id=\"fs-id1167833049694\">\n<p id=\"fs-id1167829849522\">Draw a sketch of the square and cube functions. What are the similarities and differences in the graphs?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167833057322\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1167829599017\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167830077412\" data-alt=\"The figure shows a table with four rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cuse the vertical line test\u201d, \u201cidentify graphs of basic functions\u201d, and \u201cread information from a graph\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_219_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with four rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cuse the vertical line test\u201d, \u201cidentify graphs of basic functions\u201d, and \u201cread information from a graph\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved\" \/><\/span><\/p>\n<p id=\"fs-id1167836729385\"><span class=\"token\">\u24d1<\/span> After reviewing this checklist, what will you do to become confident for all objectives?<\/p>\n<\/div>\n<\/div>\n<div class=\"review-exercises\" data-depth=\"1\" id=\"fs-id1167836524742\">\n<h3 data-type=\"title\">Chapter Review Exercises<\/h3>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824674139\">\n<h4 data-type=\"title\"><a href=\"\/contents\/26e8f94c-1f76-46ec-8e6c-344f06971cf5\" class=\"target-chapter\">Graph Linear Equations in Two Variables<\/a><\/h4>\n<p id=\"fs-id1167836689070\"><strong data-effect=\"bold\">Plot Points in a Rectangular Coordinate System<\/strong><\/p>\n<p id=\"fs-id1167833059130\">In the following exercises, plot each point in a rectangular coordinate system.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836560058\">\n<div data-type=\"problem\" id=\"fs-id1167836560060\">\n<p id=\"fs-id1167829595121\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d66960a9b4adfa7702388a061d743cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-862a9525ac8db19009bf877fff4597b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-cce39ff68b5344b16ea252f5e341335b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836300056\"><span data-type=\"media\" id=\"fs-id1167829621293\" data-alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_349_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167833329338\">\n<p id=\"fs-id1167829785790\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-28a186f2424d2e935d6aa6388441b6d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167836408579\">In the following exercises, determine which ordered pairs are solutions to the given equations.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836728880\">\n<div data-type=\"problem\" id=\"fs-id1167833271954\">\n<p id=\"fs-id1167833271956\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f6eff18762579051cd1137cae725d1e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#121;&#61;&#49;&#48;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b932df7404bba7c4812c40fc6d0d4b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1d3cebae54c0b7ca010cd0d379d1edda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833020246\">\n<p id=\"fs-id1167833020249\"><span class=\"token\">\u24d1<\/span>, <span class=\"token\">\u24d2<\/span><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829644642\">\n<div data-type=\"problem\" id=\"fs-id1167836549257\">\n<p id=\"fs-id1167836614945\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fb5a850cf361e867e98796edf9f73bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#54;&#120;&#45;&#50;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-28e430bac2aa969c43ac059098206ec7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e228594fa0479f071602af78e20058a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167836667122\"><strong data-effect=\"bold\">Graph a Linear Equation by Plotting Points<\/strong><\/p>\n<p id=\"fs-id1167829785046\">In the following exercises, graph by plotting points.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836423872\">\n<div data-type=\"problem\" id=\"fs-id1167836523530\">\n<p id=\"fs-id1167836523532\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-da6fdd764c10cd72cb8a7592107763ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829628246\"><span data-type=\"media\" id=\"fs-id1167829850431\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_351_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833326537\">\n<div data-type=\"problem\" id=\"fs-id1167836686054\">\n<p id=\"fs-id1167836686056\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ae17fd29062052621010e587cc571ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829859281\">\n<div data-type=\"problem\" id=\"fs-id1167829859283\">\n<p id=\"fs-id1167824648946\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4e2ae707ab5eccd1febc4c89a755aa4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829890835\"><span data-type=\"media\" id=\"fs-id1167833138261\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_353_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836624857\">\n<div data-type=\"problem\" id=\"fs-id1167836624859\">\n<p id=\"fs-id1167833378492\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6ea212d3edc781d4492da65c06ed06be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826169944\">\n<div data-type=\"problem\" id=\"fs-id1167829919797\">\n<p id=\"fs-id1167833379178\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-dd41422f1ac22abfc0b066778966a249_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836495112\"><span data-type=\"media\" id=\"fs-id1167833208030\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_355_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836705576\">\n<div data-type=\"problem\" id=\"fs-id1167836705579\">\n<p id=\"fs-id1167836529723\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f6eee09e6757335b61d3135eead59dc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829688321\">\n<div data-type=\"problem\" id=\"fs-id1167836689329\">\n<p id=\"fs-id1167833050658\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4fa0b37b12e2ed9b6d126e5523cd6dbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167829880330\" data-alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_357_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167836296637\"><strong data-effect=\"bold\">Graph Vertical and Horizontal lines<\/strong><\/p>\n<p id=\"fs-id1167833019205\">In the following exercises, graph each equation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829861802\">\n<div data-type=\"problem\" id=\"fs-id1167826131102\">\n<p id=\"fs-id1167826131104\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836698868\">\n<div data-type=\"problem\" id=\"fs-id1167832999780\">\n<p id=\"fs-id1167832999782\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836628586\"><span data-type=\"media\" id=\"fs-id1167829853783\" data-alt=\"This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_359_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167833207874\">In the following exercises, graph each pair of equations in the same rectangular coordinate system.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836611473\">\n<div data-type=\"problem\" id=\"fs-id1167836429498\">\n<p id=\"fs-id1167836429500\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b1860f3bc1742115ef9046a1238467de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836407159\">\n<div data-type=\"problem\" id=\"fs-id1167829596805\">\n<p id=\"fs-id1167829596808\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f1e7a07495bee2d0756082ab9ee676cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-70b549b23d0269e0c4ccef7a5db57f1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167829810794\" data-alt=\"The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_361_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167824578489\"><strong data-effect=\"bold\">Find <em data-effect=\"italics\">x-<\/em> and <em data-effect=\"italics\">y-<\/em>Intercepts<\/strong><\/p>\n<p id=\"fs-id1167836340022\">In the following exercises, find the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-intercepts.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836692041\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836692043\"><span data-type=\"media\" id=\"fs-id1167829840769\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 2), (0, 4), (2, 6), and (4, 8).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_220_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 2), (0, 4), (2, 6), and (4, 8).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829751646\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829751648\"><span data-type=\"media\" id=\"fs-id1167833056929\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 4), (0, 3), (3, 0), and (6, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_221_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 4), (0, 3), (3, 0), and (6, negative 3).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833024082\">\n<p id=\"fs-id1167836356293\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-713286d4551c797296acce493b2ddc56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833369799\">In the following exercises, find the intercepts of each equation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836627814\">\n<div data-type=\"problem\" id=\"fs-id1167829586489\">\n<p id=\"fs-id1167836391526\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a5997265c66b87439045a6e55e1895e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836514020\">\n<div data-type=\"problem\" id=\"fs-id1167836514023\">\n<p id=\"fs-id1167836691368\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-57266acf353f74b1688f614aa9924f89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836729649\">\n<p id=\"fs-id1167836729651\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b6be100063f95bced032b9d0ccb5d887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836697400\">\n<div data-type=\"problem\" id=\"fs-id1167836697402\">\n<p id=\"fs-id1167833004921\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-81bf3fe4432aa807b30107962af3db18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824737382\">\n<div data-type=\"problem\" id=\"fs-id1167824737384\">\n<p id=\"fs-id1167829720692\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6c184dd0067a07cf1a40243ff0b06277_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"93\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836386913\">\n<p id=\"fs-id1167836386915\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5e33f7fa868b5b2e8d9a770ca5c0d9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836537272\">\n<div data-type=\"problem\" id=\"fs-id1167833407393\">\n<p id=\"fs-id1167833407395\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-90a3bd9d443d8f417af939f7c60966d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829595359\"><strong data-effect=\"bold\">Graph a Line Using the Intercepts<\/strong><\/p>\n<p id=\"fs-id1167829906596\">In the following exercises, graph using the intercepts.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829877972\">\n<div data-type=\"problem\" id=\"fs-id1167824737270\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5ba7e81926f96fc690061f2050dd4bd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;&#43;&#51;&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833339919\"><span data-type=\"media\" id=\"fs-id1167836559721\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_362_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833057045\">\n<div data-type=\"problem\" id=\"fs-id1167824731739\">\n<p id=\"fs-id1167829905654\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-34369662c27bc734321912f8c566ce3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824648910\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167829586204\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9a41264b7e0167afdfa6a5d86537c936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829851580\"><span data-type=\"media\" id=\"fs-id1167829597299\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_364_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836509101\">\n<div data-type=\"problem\" id=\"fs-id1167836423881\">\n<p id=\"fs-id1167836423883\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b17d88f3ef2c272cc2a5f53f5d8888a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#52;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836626758\">\n<div data-type=\"problem\" id=\"fs-id1167836507734\">\n<p id=\"fs-id1167833380731\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3830f1c4beca3ad0dd7e3a5dae581de2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836513855\"><span data-type=\"media\" id=\"fs-id1167829755848\" data-alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_366_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167829740806\">\n<h4 data-type=\"title\"><a href=\"\/contents\/c7953cb6-51e3-48e7-9969-821f34daec42\" class=\"target-chapter\">Slope of a Line<\/a><\/h4>\n<p id=\"fs-id1167833047231\"><strong data-effect=\"bold\">Find the Slope of a Line<\/strong><\/p>\n<p id=\"fs-id1167836540143\">In the following exercises, find the slope of each line shown.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836366545\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836620203\"><span data-type=\"media\" id=\"fs-id1167836620205\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, 0) and (1, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_222_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, 0) and (1, negative 3).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829691193\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829788714\"><span data-type=\"media\" id=\"fs-id1167829788716\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, 0) and (0, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_223_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, 0) and (0, 4).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833175418\">\n<p id=\"fs-id1167833366014\">1<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836790118\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836790120\"><span data-type=\"media\" id=\"fs-id1167832980890\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, negative 4) and (2, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_224_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, negative 4) and (2, negative 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836623132\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836623134\"><span data-type=\"media\" id=\"fs-id1167829905380\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (1, 4) and (5, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_225_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (1, 4) and (5, 2).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829690312\">\n<p id=\"fs-id1167829690314\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-413f537f0ad6eef7c0df18690b364ca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836738035\">In the following exercises, find the slope of each line.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833086454\">\n<div data-type=\"problem\" id=\"fs-id1167833036675\">\n<p id=\"fs-id1167833036677\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836399770\">\n<div data-type=\"problem\" id=\"fs-id1167836399772\">\n<p id=\"fs-id1167832945666\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836512350\">\n<p id=\"fs-id1167836356549\">undefined<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836398874\">\n<div data-type=\"problem\" id=\"fs-id1167836606570\">\n<p id=\"fs-id1167836606572\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829578786\">\n<div data-type=\"problem\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836652641\">\n<p id=\"fs-id1167833224570\">0<\/p>\n<\/div>\n<\/div>\n<p><strong data-effect=\"bold\">Use the Slope Formula to find the Slope of a Line between Two Points<\/strong><\/p>\n<p id=\"fs-id1167829931428\">In the following exercises, use the slope formula to find the slope of the line between each pair of points.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167824734049\">\n<div data-type=\"problem\" id=\"fs-id1167836664452\">\n<p id=\"fs-id1167836664454\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-afe984809a9a5798db58c2a9a45c9ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836322980\">\n<div data-type=\"problem\" id=\"fs-id1167836322982\">\n<p id=\"fs-id1167829790349\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-878e26f307e1cc660f5d012d708a8655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833049600\">\n<p id=\"fs-id1167836455885\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836738195\">\n<div data-type=\"problem\" id=\"fs-id1167836738198\">\n<p id=\"fs-id1167825766169\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-137dfb5207d8acfcc772b3457aab688e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836391480\">\n<div data-type=\"problem\" id=\"fs-id1167836391482\">\n<p id=\"fs-id1167833310349\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a770678d45991595ad8a2eb5c49b8649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836673408\">\n<p id=\"fs-id1167836673410\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3c8a34714cd9e14f96438eaca16625df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836387581\"><strong data-effect=\"bold\">Graph a Line Given a Point and the Slope<\/strong><\/p>\n<p id=\"fs-id1167829714127\">In the following exercises, graph each line with the given point and slope.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836620933\">\n<div data-type=\"problem\" id=\"fs-id1167836620935\">\n<p id=\"fs-id1167829685902\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3e2d4fab5e437f4c621efe487421c415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0a0d1402bbb7832b87b9cb01de90be0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829717719\">\n<div data-type=\"problem\" id=\"fs-id1167832980872\">\n<p id=\"fs-id1167832980874\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-90230e505516d9de65de61c2df538bcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6fae7ea410efdec23083d9f11b3cee98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836408863\"><span data-type=\"media\" id=\"fs-id1167836408866\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_368_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829878927\">\n<div data-type=\"problem\" id=\"fs-id1167836557400\">\n<p id=\"fs-id1167836557402\"><em data-effect=\"italics\">x<\/em>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-33b72ef21b26741cca074584bd6ba53e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: -3px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-260107cba86a7b21e919180b1130050e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836536584\">\n<div data-type=\"problem\" id=\"fs-id1167836536586\">\n<p id=\"fs-id1167829693217\"><em data-effect=\"italics\">y<\/em>-intercept 1; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c1c682827dbbd6233dceaa20c8d888f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836540579\"><span data-type=\"media\" id=\"fs-id1167836540582\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_370_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167829783830\"><strong data-effect=\"bold\">Graph a Line Using Its Slope and Intercept<\/strong><\/p>\n<p>In the following exercises, identify the slope and <em data-effect=\"italics\">y<\/em>-intercept of each line.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836524200\">\n<div data-type=\"problem\" id=\"fs-id1167833369422\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6f04888ecfc66a9974bfaad65f815ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836434016\">\n<div data-type=\"problem\" id=\"fs-id1167836434018\">\n<p id=\"fs-id1167836392639\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5e7d237209747776f0a458f4fab43b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836575631\">\n<p id=\"fs-id1167836575633\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6f2fa762d114591844f5c8e04e9d6d6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"110\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836507861\">\n<div data-type=\"problem\" id=\"fs-id1167833256025\">\n<p id=\"fs-id1167833256027\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-094461e36cb826a192135218c9d23e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829741996\">\n<div data-type=\"problem\" id=\"fs-id1167829741998\">\n<p id=\"fs-id1167829619884\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ce40bea7fe053c8359dd89391934690c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#53;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833054991\">\n<p id=\"fs-id1167836526730\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-270e5f165025cf701587dbc6aae03824_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#59;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"113\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836312931\">In the following exercises, graph the line of each equation using its slope and <em data-effect=\"italics\">y<\/em>-intercept.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836558639\">\n<div data-type=\"problem\" id=\"fs-id1167836408213\">\n<p id=\"fs-id1167836408215\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bcf5730024e3060d723a9a8b68ef7ec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836533072\">\n<div data-type=\"problem\" id=\"fs-id1167832982331\">\n<p id=\"fs-id1167832982333\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b1392cadd41dc6e5dd89c82dcd291ecd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836375314\"><span data-type=\"media\" id=\"fs-id1167833270225\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_372_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836598001\">\n<p id=\"fs-id1167836598003\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-215399458b646bed9c7b04dfcc7da927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836535018\">\n<p id=\"fs-id1167836535020\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-efedfb1adc9ce250cfc862e4fb07e730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833340136\"><span data-type=\"media\" id=\"fs-id1167836493581\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_374_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167836558141\">In the following exercises, determine the most convenient method to graph each line.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836509786\">\n<div data-type=\"problem\" id=\"fs-id1167836509788\">\n<p id=\"fs-id1167824578768\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829952812\">\n<div data-type=\"problem\" id=\"fs-id1167825766095\">\n<p id=\"fs-id1167825766097\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836597617\">\n<p id=\"fs-id1167836597619\">horizontal line<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833060079\">\n<div data-type=\"problem\" id=\"fs-id1167833060081\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1e79103209b195d55f301e7f6bd76c17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833059952\">\n<div data-type=\"problem\" id=\"fs-id1167833059954\">\n<p id=\"fs-id1167829715877\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9a5b3c22bb39414b75fba2f7f523204b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836697072\">\n<p id=\"fs-id1167829787194\">intercepts<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836575255\">\n<p id=\"fs-id1167836575257\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ff12e29ca00d44061ed97e665ff0cff2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#125;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836525357\">\n<div data-type=\"problem\" id=\"fs-id1167836525359\">\n<p id=\"fs-id1167824766879\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-026f9b7b2b0e9b43f47498f70dddbe90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833138013\">\n<p id=\"fs-id1167833138015\">plotting points<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836527756\"><strong data-effect=\"bold\">Graph and Interpret Applications of Slope-Intercept<\/strong><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167826211804\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167826211806\">\n<p id=\"fs-id1167836717304\">Katherine is a private chef. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6a559403a1874bfd4618efd8303f8845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#54;&#46;&#53;&#109;&#43;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"114\" style=\"vertical-align: -2px;\" \/> models the relation between her weekly cost, <em data-effect=\"italics\">C<\/em>, in dollars and the number of meals, <em data-effect=\"italics\">m<\/em>, that she serves.<\/p>\n<p id=\"fs-id1167836440780\"><span class=\"token\">\u24d0<\/span> Find Katherine\u2019s cost for a week when she serves no meals.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find the cost for a week when she serves 14 meals.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Interpret the slope and <em data-effect=\"italics\">C<\/em>-intercept of the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Graph the equation.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829709310\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829709313\">\n<p id=\"fs-id1167829694607\">Marjorie teaches piano. The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c1fccf8079e4ef736fa47bbb966e40ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#51;&#53;&#104;&#45;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"114\" style=\"vertical-align: 0px;\" \/> models the relation between her weekly profit, <em data-effect=\"italics\">P<\/em>, in dollars and the number of student lessons, <em data-effect=\"italics\">s<\/em>, that she teaches.<\/p>\n<p><span class=\"token\">\u24d0<\/span> Find Marjorie\u2019s profit for a week when she teaches no student lessons.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find the profit for a week when she teaches 20 student lessons.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Interpret the slope and <em data-effect=\"italics\">P<\/em>-intercept of the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Graph the equation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830123744\">\n<p id=\"fs-id1167830123746\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-24d1a352dc8448416d9c6bf378ef3c45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> ?450<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> The slope, 35, means that Marjorie\u2019s weekly profit, <em data-effect=\"italics\">P<\/em>, increases by ?35 for each additional student lesson she teaches.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> The <em data-effect=\"italics\">P<\/em>-intercept means that when the number of lessons is 0, Marjorie loses ?250.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span data-type=\"media\" id=\"fs-id1167833050702\" data-alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_376_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167833350392\"><strong data-effect=\"bold\">Use Slopes to Identify Parallel and Perpendicular Lines<\/strong><\/p>\n<p id=\"fs-id1167836705885\">In the following exercises, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836730415\">\n<div data-type=\"problem\" id=\"fs-id1167836730417\">\n<p id=\"fs-id1167833060992\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3b34f08a033be0c9813275fb0f636443_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#121;&#61;&#45;&#49;&#59;&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"198\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836499090\">\n<div data-type=\"problem\" id=\"fs-id1167836499092\">\n<p id=\"fs-id1167833408067\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bc0252f40df68651ac6baca514305500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;&#59;&#49;&#48;&#120;&#43;&#50;&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829833842\">\n<p id=\"fs-id1167829833844\">neither<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836717592\">\n<div data-type=\"problem\" id=\"fs-id1167836717594\">\n<p id=\"fs-id1167833239045\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b74bfed1787b29274b1408cae61d1a02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#50;&#121;&#61;&#53;&#59;&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836792421\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836575517\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f1222ac00007ebd636eddfb3e358efae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#121;&#61;&#56;&#59;&#120;&#45;&#50;&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836601367\">\n<p id=\"fs-id1167836601369\">not parallel<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836526512\">\n<h4 data-type=\"title\"><a href=\"\/contents\/a70487c0-0cc1-4b9b-bed5-8c15bf231b19\" class=\"target-chapter\">Find the Equation of a Line<\/a><\/h4>\n<p id=\"fs-id1167836613250\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and <em data-effect=\"italics\">y<\/em>-Intercept<\/strong><\/p>\n<p id=\"fs-id1167829861813\">In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167832937076\">\n<div data-type=\"problem\" id=\"fs-id1167836536612\">\n<p id=\"fs-id1167836536614\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-34f0e870957984f6c69249b8cf4f5813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-76ba30a779b2946f1d9c14bf4ce7c710_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833334748\">\n<div data-type=\"problem\" id=\"fs-id1167829597265\">\n<p id=\"fs-id1167829597267\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826212238\">\n<p id=\"fs-id1167826212240\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-beb1b3bee4702cfeed1e5896d93bd530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829597408\">\n<div data-type=\"problem\" id=\"fs-id1167829597410\">\n<p id=\"fs-id1167829716068\">slope 0 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824732674\">\n<div data-type=\"problem\">\n<p>slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836327049\">\n<p id=\"fs-id1167836327051\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b1860f3bc1742115ef9046a1238467de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829744040\">In the following exercises, find the equation of the line shown in each graph. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833025723\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829746479\"><span data-type=\"media\" id=\"fs-id1167829746482\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_226_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824733731\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836599996\"><span data-type=\"media\" id=\"fs-id1167836599999\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_227_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836512155\">\n<p id=\"fs-id1167829751092\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9ca7e6824e1b3783daf117b3e7f97530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829597335\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829693762\"><span data-type=\"media\" id=\"fs-id1167829693765\" data-alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_228_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829921267\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836434329\"><span data-type=\"media\" id=\"fs-id1167836434331\" data-alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_229_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836549401\">\n<p id=\"fs-id1167833086867\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833346720\"><strong data-effect=\"bold\">Find an Equation of the Line Given the Slope and a Point<\/strong><\/p>\n<p id=\"fs-id1167829718877\">In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833041788\">\n<p id=\"fs-id1167833041790\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b7dbe9c3e3bf7e12328fdd79cf7c3d63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c031b585aaf171a727861c193b59e4cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829596447\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829596449\">\n<p id=\"fs-id1167833175513\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e34339c2ae9eb73cf9ad6c31e6fffc2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1f1d2e6666cb0e1b607fd15a9e16506d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836645860\">\n<p id=\"fs-id1167836645862\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-96a303128b4436218d0ab559f9d80278_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836684568\">\n<p id=\"fs-id1167836684570\">Horizontal line containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-374b47fb7bf10f554c21530f0ecc88e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829756252\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829756254\">\n<p id=\"fs-id1167829756256\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d4591560f9596f4d951571ae42ac44c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#45;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836439630\">\n<p id=\"fs-id1167836439632\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d70d1bb18e48ec7aa6574590e6e70184_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p><strong data-effect=\"bold\">Find an Equation of the Line Given Two Points<\/strong><\/p>\n<p id=\"fs-id1167833086732\">In the following exercises, find the equation of a line containing the given points. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836550894\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836550896\">\n<p id=\"fs-id1167829789152\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-16713c912b1421f18499c8a340ac1e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03df60c183567a5ad79ee9c595898add_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826169452\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167830093792\">\n<p id=\"fs-id1167830093794\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f63e6ea0c8474555192b305e3472481d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e3e1928d65786877c787a2d401d9e77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836614917\">\n<p id=\"fs-id1167836613350\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8246b420a6c90bc8e66b3245ebb1f0ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829749597\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829749599\">\n<p id=\"fs-id1167829749601\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aa1e37a09fb9a2a365196b061a17f1fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-abcb6ace4b542ff0928998579e86da44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824734798\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824734800\">\n<p id=\"fs-id1167824734802\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3d8ac8f4b342f0dbc31733d2d4443ce9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aeaca1910c48ce1d63188a726ff94fc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167833021593\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829596630\"><strong data-effect=\"bold\">Find an Equation of a Line Parallel to a Given Line<\/strong><\/p>\n<p id=\"fs-id1167836366759\">In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829784008\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829784010\">\n<p id=\"fs-id1167829784012\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-49e65fa83a2bc69f2d1f6af64ac8ecb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-91e09d029e9b798ea0b0617171c88cca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836535046\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833339170\">\n<p id=\"fs-id1167833339172\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-879f187e9109d6082c627a589808536f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#53;&#121;&#61;&#45;&#49;&#48;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a8241b8ef917fd8c90843ad0ff9220b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6894f39f5ba0b077abb0580c55a1bbcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836538320\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836538322\">\n<p id=\"fs-id1167836538324\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9ad850560a1ff3e3bb4386cf732d0220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ef9b0ead245d0b508218b1cb59d48442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829930155\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829930157\">\n<p id=\"fs-id1167833345935\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-649b5aebdf42aa0c48eb8b8d2ffedda8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4d4c06de3c48d63deaeaa1d43ed2ba09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167833340114\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833129252\"><strong data-effect=\"bold\">Find an Equation of a Line Perpendicular to a Given Line<\/strong><\/p>\n<p id=\"fs-id1167824585096\">In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope\u2013intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167824734676\" class=\"material-set-2\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167829743859\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-35f7251a2e38988fac0111ed5d73d75c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#120;&#43;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"102\" style=\"vertical-align: -6px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b19b0a80340e51690e093dbf76e64830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836687826\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836687828\">\n<p id=\"fs-id1167825003616\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-729ad6339cdc44f5454633df59dbfcc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#51;&#121;&#61;&#57;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-91357ad9f837f690ca370a0ee126647e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829693413\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d4fa7215ff0fd90ed9093e3c5f9f1d17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824739288\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824739290\">\n<p id=\"fs-id1167825857164\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3de476f3f4a9c131a1bdbfb22329e740_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836686948\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829627590\">\n<p id=\"fs-id1167829627592\">line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-bb160c5e6177bdd7a1d220c410258e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829721210\">\n<p id=\"fs-id1167829721212\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0e3ca3f6eb8810e090b4ceee7f6e129b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836570304\">\n<h4 data-type=\"title\"><a href=\"\/contents\/f15d09b6-aae4-4ad3-a9e6-c9d1ac2436e3\" class=\"target-chapter\">Graph Linear Inequalities in Two Variables<\/a><\/h4>\n<p id=\"fs-id1167832951212\"><strong data-effect=\"bold\">Verify Solutions to an Inequality in Two Variables<\/strong><\/p>\n<p id=\"fs-id1167833272639\">In the following exercises, determine whether each ordered pair is a solution to the given inequality.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833052460\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833052463\">\n<p id=\"fs-id1167833052465\">Determine whether each ordered pair is a solution to the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-52e61dce18ea683f0d0a29e38a367058_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#60;&#120;&#45;&#51;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ecc91b8d5e91ea23c08fcf2ee52342c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3d8ac8f4b342f0dbc31733d2d4443ce9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0d66a71b8940b998e4f29f8cccda06d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d66960a9b4adfa7702388a061d743cbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833379475\">\n<p id=\"fs-id1167836622804\">Determine whether each ordered pair is a solution to the inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4d4047f5388385b7162178177ff267ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#62;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167836792019\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fc9db18ceda8b325515059e9c425b44f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7bb2826a2e30fc68ca873be9bb345e80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f3b8ee106f7e5a95f1dd3e0ab5f16435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b4bbfc3f28d7c93817d788ac66472798_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836621307\">\n<p id=\"fs-id1167836621309\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> no <span class=\"token\">\u24d2<\/span> yes <span class=\"token\">\u24d3<\/span> yes; <span class=\"token\">\u24d4<\/span> no<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833057530\"><strong data-effect=\"bold\">Recognize the Relation Between the Solutions of an Inequality and its Graph<\/strong><\/p>\n<p id=\"fs-id1167836312912\">In the following exercises, write the inequality shown by the shaded region.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167824841358\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824841360\">\n<p id=\"fs-id1167824841363\">Write the inequality shown by the graph with the boundary line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4cf1bfc146b9132de958d9b4fc2b0446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167833381869\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 2), (1, 1), and (2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_230_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 2), (1, 1), and (2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836515439\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836515442\">\n<p id=\"fs-id1167836694224\">Write the inequality shown by the graph with the boundary line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a55460f61789c2fcc49bc683ccf8275d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836621666\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (3, negative 1), and (6, 1). The line divides the x y-coordinate plane into two halves. The line and the top left half are shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_231_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (3, negative 1), and (6, 1). The line divides the x y-coordinate plane into two halves. The line and the top left half are shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836432878\">\n<p id=\"fs-id1167833136729\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c8fa5cd951cb3747c8446d0af09f93b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#62;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"85\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829688943\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829688945\">\n<p id=\"fs-id1167836326696\">Write the inequality shown by the shaded region in the graph with the boundary line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-dccfc3e58f9f61b86468cd40e7d7065e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#61;&#45;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167833361642\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (negative 2, negative 2), and (negative 4, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_232_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (negative 2, negative 2), and (negative 4, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832982202\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167832982205\">\n<p>Write the inequality shown by the shaded region in the graph with the boundary line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6a4988221135dbcfd378991b67150f01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#121;&#61;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836535109\" data-alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (2, negative 2), and (6, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_233_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (2, negative 2), and (6, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836701518\">\n<p id=\"fs-id1167836701520\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e5870ff5079c46655f381f7167497a95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#50;&#121;&#92;&#103;&#101;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836509955\"><strong data-effect=\"bold\">Graph Linear Inequalities in Two Variables<\/strong><\/p>\n<p id=\"fs-id1167829921248\">In the following exercises, graph each linear inequality.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829921251\">\n<div data-type=\"problem\" id=\"fs-id1167836392054\">\n<p id=\"fs-id1167836392056\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a2034b509cccef24f20a827607e53645_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#62;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#120;&#45;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833237777\">\n<div data-type=\"problem\" id=\"fs-id1167833237779\">\n<p id=\"fs-id1167833237782\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-206efc9684593f8a3d895b1a4153f14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#108;&#101;&#32;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#120;&#43;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"102\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\"><span data-type=\"media\" id=\"fs-id1167832937170\" data-alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_378_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836495549\">\n<p id=\"fs-id1167836495551\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-eb7ea8fa95d4932503bc5c99d2d10df6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#92;&#108;&#101;&#32;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836341917\">\n<div data-type=\"problem\" id=\"fs-id1167836341919\">\n<p id=\"fs-id1167829783814\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-86476c5ea410623a5daa993526a8065e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#62;&#49;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836620995\"><span data-type=\"media\" id=\"fs-id1167836729455\" data-alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_380_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836497114\">\n<div data-type=\"problem\" id=\"fs-id1167836497116\">\n<p id=\"fs-id1167836497118\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c6e37a26ba6848a897f03dc88395c500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#108;&#101;&#32;&#45;&#51;&#120;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833237757\">\n<div data-type=\"problem\" id=\"fs-id1167829719800\">\n<p id=\"fs-id1167829719802\">Graph the linear inequality <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-04a402f80ad20e5eb612f65b2b662387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#60;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829747740\"><span data-type=\"media\" id=\"fs-id1167836530484\" data-alt=\"This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_382_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167824734423\"><strong data-effect=\"bold\">Solve Applications using Linear Inequalities in Two Variables<\/strong><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836567301\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836567303\">\n<p id=\"fs-id1167836567305\">Shanthie needs to earn at least ?500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays ?10 an hour and the other as an intern in a law office for ?25 hour. How many hours does Shanthie need to work at each job to earn at least ?500 per week?<\/p>\n<p id=\"fs-id1167824734612\"><span class=\"token\">\u24d0<\/span> Let <em data-effect=\"italics\">x<\/em> be the number of hours she works teaching swimming and let <em data-effect=\"italics\">y<\/em> be the number of hours she works as an intern. Write an inequality that would model this situation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Graph the inequality.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find three ordered pairs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> that would be solutions to the inequality. Then, explain what that means for Shanthie.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836409564\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836409567\">\n<p id=\"fs-id1167836553948\">Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking.<\/p>\n<p id=\"fs-id1167836553953\"><span class=\"token\">\u24d0<\/span> If <em data-effect=\"italics\">x<\/em> is the number of minutes that Atsushi runs and <em data-effect=\"italics\">y<\/em> is the number minutes he bikes, find the inequality that models the situation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Graph the inequality.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> List three solutions to the inequality. What options do the solutions provide Atsushi?<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829704678\">\n<p id=\"fs-id1167829704681\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-919820a780b54735ec724441797c0ef5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#120;&#43;&#49;&#53;&#121;&#92;&#103;&#101;&#32;&#54;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829594005\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_384_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> Answers will vary.<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167826172554\">\n<h4 data-type=\"title\"><a href=\"\/contents\/5e548626-8f0f-496d-ab87-4f0358ca2fd3\" class=\"target-chapter\">Relations and Functions<\/a><\/h4>\n<p id=\"fs-id1167836486019\"><strong data-effect=\"bold\">Find the Domain and Range of a Relation<\/strong><\/p>\n<p id=\"fs-id1167833365925\">In the following exercises, for each relation, <span class=\"token\">\u24d0<\/span> find the domain of the relation <span class=\"token\">\u24d1<\/span> find the range of the relation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833056137\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833056139\">\n<p id=\"fs-id1167836717056\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7f6a0cf7ab36830b149ccd71b5cd43ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c12c16573392d7b657c4122d358ded16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#44;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833053062\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833053064\">\n<p id=\"fs-id1167836408010\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-00b019f4fe87d5bc750c8fe9a345c717_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03e2d890538d77a9bb98764ae2993efa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829908245\">\n<p id=\"fs-id1167829908247\"><span class=\"token\">\u24d0<\/span> D: {\u22123, \u22122, \u22121, 0}<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> R: {7, 3, 9, \u22123, 8}<\/div>\n<\/div>\n<p id=\"fs-id1167833346961\">In the following exercise, use the mapping of the relation to <span class=\"token\">\u24d0<\/span> list the ordered pairs of the relation <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836325788\">\n<div data-type=\"problem\" id=\"fs-id1167836325790\">\n<p id=\"fs-id1167836325792\">The mapping below shows the average weight of a child according to age.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167829685523\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cAge (yrs)\u201d and lists the numbers 1, 2, 3, 4, 5, 6, and 7. The table on the right has the header \u201cWeight (pounds)\u201d and lists the numbers 20, 35, 30, 45, 40, 25, and 50. There are arrows starting at numbers in the age table and pointing towards numbers in the weight table. The first arrow goes from 1 to 20. The second arrow goes from 2 to 25. The third arrow goes from 3 to 30. The fourth arrow goes from 4 to 35. The fifth arrow goes from 5 to 40. The sixth arrow goes from 6 to 45. The seventh arrow goes from 7 to 50.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_234_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cAge (yrs)\u201d and lists the numbers 1, 2, 3, 4, 5, 6, and 7. The table on the right has the header \u201cWeight (pounds)\u201d and lists the numbers 20, 35, 30, 45, 40, 25, and 50. There are arrows starting at numbers in the age table and pointing towards numbers in the weight table. The first arrow goes from 1 to 20. The second arrow goes from 2 to 25. The third arrow goes from 3 to 30. The fourth arrow goes from 4 to 35. The fifth arrow goes from 5 to 40. The sixth arrow goes from 6 to 45. The seventh arrow goes from 7 to 50.\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167836597962\">In the following exercise, use the graph of the relation to <span class=\"token\">\u24d0<\/span> list the ordered pairs of the relation <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836368154\">\n<div data-type=\"problem\" id=\"fs-id1167836368156\"><span data-type=\"media\" id=\"fs-id1167824617025\" data-alt=\"The figure shows the graph of some points on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The points (negative 3, 1), (negative 2, negative 1), (negative 2, negative 3), (0, negative 1), (0, 4), and (4, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_235_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows the graph of some points on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The points (negative 3, 1), (negative 2, negative 1), (negative 2, negative 3), (0, negative 1), (0, 4), and (4, 3).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833290236\">\n<p id=\"fs-id1167833290238\"><span class=\"token\">\u24d0<\/span> (4, 3), (\u22122, \u22123), (\u22122, \u22121), (\u22123, 1), (0, \u22121), (0, 4),<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: {\u22123, \u22122, 0, 4}<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> R: {\u22123, \u22121, 1, 3, 4}<\/div>\n<\/div>\n<p id=\"fs-id1167836691409\"><strong data-effect=\"bold\">Determine if a Relation is a Function<\/strong><\/p>\n<p id=\"fs-id1167836543349\">In the following exercises, use the set of ordered pairs to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function <span class=\"token\">\u24d1<\/span> find the domain of the relation <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836571217\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836487361\">\n<p id=\"fs-id1167836487363\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f2a06360443ac4b395275ad211a728e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fea828fbbf6183c3aa570fcb5ec0880b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"188\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836319254\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836319256\">\n<p id=\"fs-id1167833008455\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b92f8ea5a47b401913bb00a38b481e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"205\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3d6423c591135d1b7df4a8ac414aee2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829695005\">\n<p id=\"fs-id1167836570181\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> {0, 1, 8, 27}<\/div>\n<\/div>\n<p id=\"fs-id1167836560861\">In the following exercises, use the mapping to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function <span class=\"token\">\u24d1<\/span> find the domain of the function <span class=\"token\">\u24d2<\/span> find the range of the function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833054561\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833054563\"><span data-type=\"media\" id=\"fs-id1167836502048\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fourth power\u201d and lists the numbers 0, 1, 16, and 81. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fourth power table. The first arrow goes from negative 3 to 81. The second arrow goes from negative 2 to 16. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 16. The seventh arrow goes from 3 to 81.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_236_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fourth power\u201d and lists the numbers 0, 1, 16, and 81. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fourth power table. The first arrow goes from negative 3 to 81. The second arrow goes from negative 2 to 16. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 16. The seventh arrow goes from 3 to 81.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824585099\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824585102\"><span data-type=\"media\" id=\"fs-id1167829715306\" data-alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fifth power\u201d and lists the numbers 0, 1, 32, 243, negative 1, negative 32, and negative 243. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fifth power table. The first arrow goes from negative 3 to negative 243. The second arrow goes from negative 2 to negative 32. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 32. The seventh arrow goes from 3 to 243.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_237_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows two table that each have one column. The table on the left has the header \u201cx\u201d and lists the numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3. The table on the right has the header \u201cx to the fifth power\u201d and lists the numbers 0, 1, 32, 243, negative 1, negative 32, and negative 243. There are arrows starting at numbers in the x table and pointing towards numbers in the x to the fifth power table. The first arrow goes from negative 3 to negative 243. The second arrow goes from negative 2 to negative 32. The third arrow goes from negative 1 to 1. The fourth arrow goes from 0 to 0. The fifth arrow goes from 1 to 1. The sixth arrow goes from 2 to 32. The seventh arrow goes from 3 to 243.\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833057444\">\n<p id=\"fs-id1167824578479\"><span class=\"token\">\u24d0<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> {\u22123, \u22122, \u22121, 0, 1, 2, 3}<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> {\u2212243, \u221232, \u22121, 0, 1, 32, 243}<\/div>\n<\/div>\n<p id=\"fs-id1167824736070\">In the following exercises, determine whether each equation is a function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836628928\">\n<div data-type=\"problem\" id=\"fs-id1167836628930\">\n<p id=\"fs-id1167836628932\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d7bb26d3c9954af84f4dec11d7baa9fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833048649\">\n<div data-type=\"problem\" id=\"fs-id1167824781609\">\n<p id=\"fs-id1167824781611\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f0e2ebf2a1b63bd75c0c19696a700e4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836409422\">\n<p id=\"fs-id1167829624646\">yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829930429\">\n<div data-type=\"problem\" id=\"fs-id1167829930432\">\n<p id=\"fs-id1167829930434\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-47bdbf719e41e4cd61a7a609f53c9186_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836730447\">\n<div data-type=\"problem\" id=\"fs-id1167833060680\">\n<p id=\"fs-id1167833060682\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4b1d53b124475c894e7d7504e830fe49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836731997\">\n<p id=\"fs-id1167836600119\">yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836600124\">\n<div data-type=\"problem\" id=\"fs-id1167833059199\">\n<p id=\"fs-id1167833059202\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7ea82467800eb09d48a96941a961ddb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167826092388\"><strong data-effect=\"bold\">Find the Value of a Function<\/strong><\/p>\n<p id=\"fs-id1167833386365\">In the following exercises, evaluate the function:<\/p>\n<p id=\"fs-id1167833386368\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-dca5d7bc047aaa23a5ac85a2c257c5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b7454c1320ac593411a470ad12380405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4153ddea4dfdd594c6187304119af999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"44\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833396868\">\n<div data-type=\"problem\" id=\"fs-id1167833396870\">\n<p id=\"fs-id1167833396872\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-af28bae81b22c4c55d080683ac0a1bde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833309935\">\n<p id=\"fs-id1167833309937\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ea16cc2f2a2e0ee5853c0d99661e469a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"106\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-635142d666b85b07a2a9127bc07efbaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"68\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-75f03fe43a7b857b8e43bd654e6a5aa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#97;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836606040\">\n<div data-type=\"problem\" id=\"fs-id1167833272058\">\n<p id=\"fs-id1167833272060\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-7751d144f04f4dcbbc1c2de64b9838e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829720100\">\n<div data-type=\"problem\" id=\"fs-id1167829720102\">\n<p id=\"fs-id1167824720473\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0dd75eeae5d794f31b6de47452d167b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167829741589\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ea5a505b78850c3c3fc9be0b45e034b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"92\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-78e0b82f195e37616b935f1e6c31f395_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1e256fd674a2e4ceedd1be520c7d6830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#97;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836389935\">\n<div data-type=\"problem\" id=\"fs-id1167824734626\">\n<p id=\"fs-id1167824734628\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-4de456b8a71a1996b53da3ed174d3205_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836614042\">In the following exercises, evaluate the function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836614045\">\n<div data-type=\"problem\" id=\"fs-id1167836614047\">\n<p id=\"fs-id1167836484624\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6e6930f105f79e141da0fdcfed96f0e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b42d35fe562a099584b3845d1d6c833c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836533819\">\n<p id=\"fs-id1167836533821\">2<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836560606\">\n<div data-type=\"problem\" id=\"fs-id1167836560608\">\n<p id=\"fs-id1167829741858\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f8c2a56201027ed936b767d0f00acf7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#49;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ab702bb67c5a96b46350e837c6fdd8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826171731\">\n<div data-type=\"problem\" id=\"fs-id1167826171733\">\n<p id=\"fs-id1167826171735\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fb4cc61bec262a4735c7c054e07d5f24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#124;&#116;&#45;&#49;&#124;&#43;&#50;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"147\" style=\"vertical-align: -4px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e055b9962584402549fc214e22fab623_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829751601\">\n<p id=\"fs-id1167829580281\">18<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829786785\">\n<div data-type=\"problem\" id=\"fs-id1167829786787\">\n<p id=\"fs-id1167829786789\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c85caccd383b393066ef0cf84daa5092_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#50;&#125;&#123;&#120;&#45;&#49;&#125;&#59;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"94\" style=\"vertical-align: -7px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b7454c1320ac593411a470ad12380405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836699953\">\n<h4 data-type=\"title\"><a href=\"\/contents\/da9d6ce0-a078-4ca2-97af-8cb374f040f5\" class=\"target-chapter\">Graphs of Functions<\/a><\/h4>\n<p id=\"fs-id1167836597214\"><strong data-effect=\"bold\">Use the Vertical line Test<\/strong><\/p>\n<p id=\"fs-id1167836664665\">In the following exercises, determine whether each graph is the graph of a function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836664668\">\n<div data-type=\"problem\" id=\"fs-id1167833224393\"><span data-type=\"media\" id=\"fs-id1167833224396\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_238_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836449375\">\n<p id=\"fs-id1167829579813\">yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832925451\">\n<div data-type=\"problem\" id=\"fs-id1167832925454\"><span data-type=\"media\" id=\"fs-id1167832925456\" data-alt=\"The figure has an s-shaped function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curve goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_239_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an s-shaped function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curve goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833082044\">\n<div data-type=\"problem\" id=\"fs-id1167833082046\"><span data-type=\"media\" id=\"fs-id1167833082048\" data-alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 5, 0), (5, 0), (0, negative 5), and (0, 5).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_240_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 5, 0), (5, 0), (0, negative 5), and (0, 5).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836391903\">\n<p id=\"fs-id1167836391905\">no<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836599515\">\n<div data-type=\"problem\" id=\"fs-id1167836599517\"><span data-type=\"media\" id=\"fs-id1167836620286\" data-alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (2, 2), and (2, negative 2). The left-most point on the graph is (negative 2, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_241_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (2, 2), and (2, negative 2). The left-most point on the graph is (negative 2, 0).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836433992\">\n<div data-type=\"problem\" id=\"fs-id1167833350356\"><span data-type=\"media\" id=\"fs-id1167833350358\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_242_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836595548\">\n<p id=\"fs-id1167833329639\">yes<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833329645\">\n<div data-type=\"problem\" id=\"fs-id1167833025417\"><span data-type=\"media\" id=\"fs-id1167833025419\" data-alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 3, 0), (negative 4, 2), and (negative 4, negative 2). The curved line on the right goes through the points (3, 0), (4, 2), and (4, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_243_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 3, 0), (negative 4, 2), and (negative 4, negative 2). The curved line on the right goes through the points (3, 0), (4, 2), and (4, negative 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836606084\">\n<div data-type=\"problem\" id=\"fs-id1167836606086\"><span data-type=\"media\" id=\"fs-id1167836606088\" data-alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, negative 1) and goes to the right. The line goes through the points (1, 0), (1, negative 2), (2, 1), and (2, negative 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_244_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, negative 1) and goes to the right. The line goes through the points (1, 0), (1, negative 2), (2, 1), and (2, negative 3).\" \/><\/span><\/div>\n<div data-type=\"solution\">\n<p>no<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836326095\"><strong data-effect=\"bold\">Identify Graphs of Basic Functions<\/strong><\/p>\n<p id=\"fs-id1167826205174\">In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range. Write the domain and range in interval notation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167832925596\">\n<div data-type=\"problem\" id=\"fs-id1167836376381\">\n<p id=\"fs-id1167836376384\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-2fcadbd61ac25bc7bf6894c208707a44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836552974\">\n<div data-type=\"problem\" id=\"fs-id1167836518717\">\n<p id=\"fs-id1167836518719\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1a8f2e01ebcf83d5a92b9cefe5e64075_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836688775\">\n<p id=\"fs-id1167836688777\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829627499\" data-alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_386_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829832341\">\n<div data-type=\"problem\" id=\"fs-id1167833020320\">\n<p id=\"fs-id1167833020322\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3259b55ecee16f078ee9aa40dfe78970_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"112\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836551845\">\n<div data-type=\"problem\" id=\"fs-id1167836551847\">\n<p id=\"fs-id1167836551849\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8844f6c69d9312b03ad087906cc5cfd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"84\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836706786\">\n<p id=\"fs-id1167829693240\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836525999\" data-alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_388_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836556410\">\n<div data-type=\"problem\" id=\"fs-id1167836556412\">\n<p id=\"fs-id1167836556414\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d268a37dadc23b636bc6955a3e233880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836523927\">\n<div data-type=\"problem\" id=\"fs-id1167836523929\">\n<p id=\"fs-id1167830093968\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db389f37d0e530d042a159db23e61866_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836429710\">\n<p id=\"fs-id1167836429712\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829692102\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_390_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,0]<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836598112\">\n<div data-type=\"problem\" id=\"fs-id1167836598114\">\n<p id=\"fs-id1167824764197\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-07274cb9949debc019c75208137fe9a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"103\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829580140\">\n<div data-type=\"problem\" id=\"fs-id1167829580143\">\n<p id=\"fs-id1167829580145\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1f5e6caca940e4789cfb81f22d83666e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836387842\">\n<p id=\"fs-id1167836387844\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836530760\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_392_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: (-\u221e,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826206199\">\n<div data-type=\"problem\" id=\"fs-id1167826206202\">\n<p id=\"fs-id1167829899546\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-866d5be9775b49e9233d3bb51965e5af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836522697\">\n<div data-type=\"problem\" id=\"fs-id1167836522699\">\n<p id=\"fs-id1167836539799\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aa15cd2c507cdbf4bd9fed5af50d861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833279763\">\n<p id=\"fs-id1167833279765\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829614418\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_394_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: [<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c3bd060f32a71334fb5cdf65d10fc75c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/> \u221e), R: [0,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830093271\">\n<div data-type=\"problem\" id=\"fs-id1167836599284\">\n<p id=\"fs-id1167836599286\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a735be45a87e6ef7a423132e7e0e735a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#124;&#120;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836282824\">\n<div data-type=\"problem\" id=\"fs-id1167836282826\">\n<p id=\"fs-id1167836282828\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c283188375e83dc1c1c38853b16cc3bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#124;&#120;&#124;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829693686\">\n<p id=\"fs-id1167829693688\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829696612\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_396_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: [1,\u221e)<\/div>\n<\/div>\n<p id=\"fs-id1167836406656\"><strong data-effect=\"bold\">Read Information from a Graph of a Function<\/strong><\/p>\n<p id=\"fs-id1167836310456\">In the following exercises, use the graph of the function to find its domain and range. Write the domain and range in interval notation<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829580264\">\n<div data-type=\"problem\" id=\"fs-id1167829580266\"><span data-type=\"media\" id=\"fs-id1167836613537\" data-alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_245_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836611953\">\n<div data-type=\"problem\" id=\"fs-id1167836611955\"><span data-type=\"media\" id=\"fs-id1167822971454\" data-alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 2). The line goes through the points (negative 1, 3) and (1, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_246_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 2). The line goes through the points (negative 1, 3) and (1, 3).\" \/><\/span><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829596916\">\n<p id=\"fs-id1167829596918\">D: (-\u221e,\u221e), R: [2,\u221e)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829984307\">\n<div data-type=\"problem\" id=\"fs-id1167836697841\"><span data-type=\"media\" id=\"fs-id1167836697843\" data-alt=\"The figure has a cubic function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 4), (0, 0), and (2, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_247_img_new-1-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cubic function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 4), (0, 0), and (2, 4).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167826077068\">In the following exercises, use the graph of the function to find the indicated values.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836445033\">\n<div data-type=\"problem\"><span data-type=\"media\" id=\"fs-id1167829748062\" data-alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_248_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.\" \/><\/span><\/p>\n<p id=\"fs-id1167836622098\"><span class=\"token\">\u24d0<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-03db5c50c4889b2ea21ecbce94fe4746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c08f879de62dd3bade0e4e3b208e2159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"72\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d6<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d7<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824720940\">\n<p id=\"fs-id1167824720942\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-55efcfcd0aed41ae0866f32b2381b3f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#47;&#125;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-55ea494ed7367544a30640e6b7689a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#112;&#105;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#47;&#125;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-506e7f62456359347409a646ee8199fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e17d900b95ffe355261eb2f5f031a00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#44;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"149\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d3e09877e24f6e27ff0a58bc8b8d53ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a07649ac45a1252fd578cabca4979249_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-825405fc63416ad0c306970366e996d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ca4d741214cce99bf41dbfe0a29e1904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6efa4463f7337cb82c0c575be91e6aba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#112;&#105;&#32;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-95b91def952d7c613d9b21978673ec31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d6<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9eca553659abf52ff7aa918edb1566c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#50;&#92;&#112;&#105;&#32;&#44;&#50;&#92;&#112;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -5px;\" \/> <span class=\"token\">\u24d7<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1948771fa2147c98ce700fec79ed4bf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#91;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#93;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832994434\">\n<div data-type=\"problem\" id=\"fs-id1167832994436\"><span data-type=\"media\" id=\"fs-id1167836439607\" data-alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0). The point (0, 2) is the highest point on the graph.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_249_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0). The point (0, 2) is the highest point on the graph.\" \/><\/span><\/p>\n<p id=\"fs-id1167832926094\"><span class=\"token\">\u24d0<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Find the values for <em data-effect=\"italics\">x<\/em> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-df88f8b453f241085be5afeee625ccb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"practice-test\" data-depth=\"1\" id=\"fs-id1167836628671\">\n<h3 data-type=\"title\">Practice Test<\/h3>\n<div data-type=\"exercise\" id=\"fs-id1167833142400\">\n<div data-type=\"problem\" id=\"fs-id1167829590736\">\n<p id=\"fs-id1167829590739\">Plot each point in a rectangular coordinate system.<\/p>\n<p id=\"fs-id1167829590742\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-2da1eb750fc283f55cb9396d5536b47a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-6b3e4a390b9705038aecd2ab7d812a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"53\" style=\"vertical-align: -7px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-e3e1928d65786877c787a2d401d9e77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836499081\"><span data-type=\"media\" id=\"fs-id1167836499084\" data-alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_397_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836556753\">\n<div data-type=\"problem\" id=\"fs-id1167836556755\">\n<p id=\"fs-id1167836300560\">Which of the given ordered pairs are solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-61d61d12705d0e557669c4942bd71bc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#121;&#61;&#54;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167836648593\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c4a2258b08828b82f5478b79177f57c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-84e35e40e916e50503f09b25572279f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836476746\">Find the slope of each line shown.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836476749\">\n<div data-type=\"problem\" id=\"fs-id1167833019700\">\n<p id=\"fs-id1167833019702\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836738269\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 5, 2) (0, negative 1), and (5, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_250_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 5, 2) (0, negative 1), and (5, negative 4).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836688572\" data-alt=\"The figure has a straight vertical line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (2, 0) (2, negative 1), and (2, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_251_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight vertical line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (2, 0) (2, negative 1), and (2, 1).\" \/><\/span><\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167833412508\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-cfb86af023a3aff3c54b9ecc49551a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/><span class=\"token\">\u24d1<\/span> undefined<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836499109\">\n<div data-type=\"problem\" id=\"fs-id1167836616459\">\n<p id=\"fs-id1167836616462\">Find the slope of the line between the points <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3d8ac8f4b342f0dbc31733d2d4443ce9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1e4e36ad4611c594832717cf011ee830_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833227002\">\n<div data-type=\"problem\" id=\"fs-id1167833227005\">\n<p id=\"fs-id1167829716790\">Graph the line with slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b8fa03e1b526c6d07ec843385490ca4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-34d359cbab98b576a127c13db3c8e58d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829785561\"><span data-type=\"media\" id=\"fs-id1167829893484\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_398_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833048332\">\n<div data-type=\"problem\" id=\"fs-id1167824725990\">\n<p id=\"fs-id1167824725992\">Find the intercepts of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a33b2bd5347596350b47752f04ae52a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#50;&#121;&#61;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"105\" style=\"vertical-align: -4px;\" \/> and graph.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833345913\"><strong data-effect=\"bold\">Graph the line for each of the following equations.<\/strong><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836514485\">\n<div data-type=\"problem\" id=\"fs-id1167836295471\">\n<p id=\"fs-id1167836295473\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a427a2c8c8d5005e2341da7519be2cb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836700038\"><span data-type=\"media\" id=\"fs-id1167836512979\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_400_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836663988\">\n<div data-type=\"problem\" id=\"fs-id1167829905989\">\n<p id=\"fs-id1167829905991\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-64c381a25fe27d286e35d4c136a53cbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836628686\">\n<div data-type=\"problem\" id=\"fs-id1167836673508\">\n<p id=\"fs-id1167836673510\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-552d8ed773e160e229551b39aff39445_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836393101\"><span data-type=\"media\" id=\"fs-id1167836393105\" data-alt=\"The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_402_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167836792029\">Find the equation of each line. Write the equation in slope-intercept form.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836792032\">\n<div data-type=\"problem\" id=\"fs-id1167829790514\">\n<p id=\"fs-id1167829790516\">slope <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aa266d939635a899a53c3c9df44a7ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"22\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercept <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829614537\">\n<div data-type=\"problem\" id=\"fs-id1167829614539\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-3638938bd00b1c4f190fd4987f3adcc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/> point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-d29d505cec09336aa569e1cca8670699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829756405\">\n<p id=\"fs-id1167833138135\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-1e76a4b2f2378c28d47bf2578fc08203_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836574822\">\n<div data-type=\"problem\" id=\"fs-id1167836574824\">\n<p id=\"fs-id1167836574826\">containing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-75bc767b0bd7cfb48fce29b6b5e7d880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-9e41965a17973324ca787678c930108f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824652819\">\n<div data-type=\"problem\" id=\"fs-id1167824652822\">\n<p id=\"fs-id1167824652824\">perpendicular to the line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-5d2d8944d236a0d6f9379d21ceac3a73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#120;&#43;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/> containing the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aad70d781c597729cec9db622e049e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-885b1b1a2bac159200697506d0b88cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836375941\">\n<div data-type=\"problem\" id=\"fs-id1167836375944\">\n<p id=\"fs-id1167836375946\">Write the inequality shown by the graph with the boundary line <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-781bd2a4e1c3b0072938dc1182b03f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836447243\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, 0), (0, negative 3), and (1, negative 4). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_252_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, 0), (0, negative 3), and (1, negative 4). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167829859341\">Graph each linear inequality.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836622063\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829893253\">\n<p id=\"fs-id1167829893255\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-419394e3e545f75f89dabad6def037d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#62;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836477414\"><span data-type=\"media\" id=\"fs-id1167833053641\" data-alt=\"The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_403_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836575646\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836575648\">\n<p id=\"fs-id1167836575650\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c9fa2dfcf0e9a249c15cf7a2d787a643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#92;&#103;&#101;&#32;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833369817\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833369819\">\n<p id=\"fs-id1167824781662\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-8d7a49d4249a9b853237f948a8d6c44b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#92;&#108;&#101;&#32;&#45;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836556454\"><span data-type=\"media\" id=\"fs-id1167829877506\" data-alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_405_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.\" \/><\/span><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833327182\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836418794\">\n<p id=\"fs-id1167836418796\">Hiro works two part time jobs in order to earn enough money to meet her obligations of at least ?450 a week. Her job at the mall pays ?10 an hour and her administrative assistant job on campus pays ?15 an hour. How many hours does Hiro need to work at each job to earn at least ?450?<\/p>\n<p id=\"fs-id1167832951073\"><span class=\"token\">\u24d0<\/span> Let <em data-effect=\"italics\">x<\/em> be the number of hours she works at the mall and let <em data-effect=\"italics\">y<\/em> be the number of hours she works as administrative assistant. Write an inequality that would model this situation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d1<\/span> Graph the inequality .<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find three ordered pairs<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> that would be solutions to the inequality. Then explain what that means for Hiro.<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833369856\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833369858\">\n<p id=\"fs-id1167833369860\">Use the set of ordered pairs to <span class=\"token\">\u24d0<\/span> determine whether the relation is a function, <span class=\"token\">\u24d1<\/span> find the domain of the relation, and <span class=\"token\">\u24d2<\/span> find the range of the relation.<\/p>\n<p id=\"fs-id1167833310998\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-06313434d539a97e39954c0f06373c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"255\" style=\"vertical-align: -5px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b6fbdd1c25c4851632ef796009f0b0e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"147\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836476899\">\n<p id=\"fs-id1167836476901\"><span class=\"token\">\u24d0<\/span> yes <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-35e16a3009070ae15d736a1bb6f347b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#45;&#51;&#44;&#45;&#50;&#44;&#45;&#49;&#44;&#48;&#44;&#49;&#44;&#50;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -5px;\" \/> <span class=\"token\">\u24d2<\/span> {0, 1, 8, 27}<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833386954\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833239798\">\n<p id=\"fs-id1167833239800\">Evaluate the function: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-134041031ac2f255a6139c40c1ff81ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-a73d5ba7eb27f0c2b0aa8c3e74588a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-77bb6761b8ea56a0f3f155df279ea752_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1167829811921\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-830922ec0420249c7033ac4521713533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833240317\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829692772\">\n<p id=\"fs-id1167829692774\">For <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-b1434f9e316a19a47da4a798f5a8cfab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#124;&#121;&#45;&#49;&#124;&#45;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"153\" style=\"vertical-align: -4px;\" \/> evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-f3fdd17e2a404cf1ec9115b6c0a5f412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832940387\">\n<p>12<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836554217\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836554219\">\n<p id=\"fs-id1167836554221\">Determine whether the graph is the graph of a function. Explain your answer.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167829715554\" data-alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_253_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).\" \/><\/span><\/div>\n<\/div>\n<p id=\"fs-id1167833223602\">In the following exercises, <span class=\"token\">\u24d0<\/span> graph each function <span class=\"token\">\u24d1<\/span> state its domain and range.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Write the domain and range in interval notation.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829831137\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829590101\">\n<p id=\"fs-id1167829590103\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-06b3023d1afd2381670ac606e243fa66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833350601\">\n<p id=\"fs-id1167836531082\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832971403\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_407_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> D: (-\u221e,\u221e), R: [1,\u221e)<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833380258\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833380261\">\n<p id=\"fs-id1167833380263\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-43c17acca432bef6d69ec5e666e5ac4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#43;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832940626\">\n<div data-type=\"problem\" id=\"fs-id1167832940628\"><span data-type=\"media\" id=\"fs-id1167832940630\" data-alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, negative 3), (0, negative 4), (1, negative 3), and (2, 0). The lowest point on the graph is (0, negative 4).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcbcintermediatealgebra\/wp-content\/uploads\/sites\/1021\/2020\/05\/CNX_IntAlg_Figure_03_06_254_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, negative 3), (0, negative 4), (1, negative 3), and (2, 0). The lowest point on the graph is (0, negative 4).\" \/><\/span><\/p>\n<p id=\"fs-id1167836629848\"><span class=\"token\">\u24d1<\/span> Find the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-intercepts.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d2<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-ecce7991a775f49b2fd6e73ef9f01226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d3<\/span> Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-85cfc02957b4ec6179fa0b580ca05891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d4<\/span> Find the domain. Write it in interval notation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p> <span class=\"token\">\u24d5<\/span> Find the range. Write it in interval notation.<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829831564\">\n<p id=\"fs-id1167833071738\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-081b622cb4fe5b0ad1b431871ee423fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;&#44;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-fa533940b92494e8365a1527736c15c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"97\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-c787289c80d86d1f0aa5eb122b9d53ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> D: (-\u221e,\u221e) <span class=\"token\">\u24d5<\/span> R: [<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-content\/ql-cache\/quicklatex.com-868764e4e7f6822206e639607822a724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/> \u221e)<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":9,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1935","chapter","type-chapter","status-publish","hentry"],"part":1405,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapters\/1935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapters\/1935\/revisions"}],"predecessor-version":[{"id":1936,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapters\/1935\/revisions\/1936"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/parts\/1405"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapters\/1935\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/wp\/v2\/media?parent=1935"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/pressbooks\/v2\/chapter-type?post=1935"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/wp\/v2\/contributor?post=1935"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/jkdcintermediatealgebracloned\/wp-json\/wp\/v2\/license?post=1935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}